This has been CNBC's live blog covering updates on the war in Ukraine. [Follow the latest updates here.]

Fighting has intensified around Ukraine's capital, Kyiv, while Russian forces bombard cities across the country, killing civilians who are unable to escape.

Russian missiles hit a military training center near Lviv, in the west of Ukraine near the Poland border, on Sunday with the number of people killed and injured rising throughout the morning.

Meanwhile, Russian forces have made some gains in their attempts to fully seize the besieged port city of Mariupol in the south of the country. Conditions in the city are dire, with civilians trapped there with limited food, water and electricity.

More than 1,500 people have died in attacks on Mariupol to date, the Associated Press reported Sunday, citing the mayor's office. Ukraine's authorities accused Russia of preventing the evacuation of civilians.

• NATO secretary general warns that Russia may use chemical weapons
• Death toll rises after Russia strikes Ukrainian military facility
• Pope Francis says 'unacceptable armed aggression' in Ukraine must stop
• Jake Sullivan and China's Yang Jiechi to discuss Ukraine on Monday

Ukraine says it shot down 8 Russian military aircraft on Sunday

Ukraine's Air Force Command claims it downed eight Russian military aircraft on Sunday, including four fixed-wing aircraft.

The command said on Facebook that it used anti-aircraft missiles to take down four planes, three helicopters and an unmanned aerial vehicle during an attack by Russian forces in the Kyiv region.

CNBC was unable to independently verify Ukraine's claim, which it made late Sunday. NBC News reported that air raid sirens sounded over Kyiv on Sunday morning.

Separately on Sunday, Russian missiles pounded a Ukraine military base near Lviv, only 20 miles (33 km) from the border with NATO nation Poland.

Ukraine officials said 35 people were killed and 135 injured in the Lviv attack.

Russian aircraft are flying 200 sorties a day, but mostly firing missiles from within Russian airspace rather than risking flights over Ukraine, according to a Friday report from military and security news site Defense One.

— Ted Kemp

China foreign affairs official and U.S. national security advisor set to meet in Rome

On Monday, U.S. national security advisor Jake Sullivan is set to meet in Rome with Yang Jiechi, director of the foreign affairs office for the Chinese Communist Party's central committee, according to official announcements.

"The two sides will discuss ongoing efforts to manage the competition between our two countries and discuss the impact of Russia's war against Ukraine on regional and global security," National Security Council spokesperson Emily Horne said in a statement.

China's Foreign Ministry spokesperson Zhao Lijian said in a statement the meeting would discuss China-U.S. relations, as well as international and regional issues of mutual concern. He did not mention Russia or Ukraine.

China has refused to call Russia's attack on Ukraine an invasion. On Friday, Premier Li Keqiang said China was "deeply" worried about the crisis.

— Evelyn Cheng

Russia reportedly asks China for assistance in invasion

Russia has asked China for military equipment to help in its invasion of Ukraine, the Financial Times reported, citing unnamed U.S. officials.

Moscow has reportedly asked for military equipment and other assistance since it began the invasion on Feb. 24, the sources said.

The U.S. government was preparing to warn allies about the situation, according to the FT report. It comes as some observers believe Russia is running out of some of its weaponry.

Moscow had expected to make far more gains and face less resistance in its attack, according to analysts. That has led to Russian President Vladimir Putin becoming increasingly frustrated, current and former U.S. officials briefed on the matter told NBC News. They warned Putin may double down on the violence as a result.

U.S. National Security Advisor Jake Sullivan is scheduled for talks Monday with China's top foreign policy official, Yang Jiechi, to discuss the invasion.

The FT reported that Sullivan is expected to warn officials that efforts to help Russia in the war or avoid sanctions would have consequences.

Read the full Financial Times report here.

—Jessica Bursztynsky

People leave notes and flowers outside the Ukraine Embassy in Washington, D.C.

People are showing their sympathy for Ukrainians with notes and flowers outside the Ukraine Embassy in Washington, D.C.

Ukraine says power has been restored to Chornobyl plant

Ukraine said a broken power line to the Chornobyl energy plant has been restored, the Associated Press reported.

The International Atomic Energy Agency (IAEA) later confirmed the news, saying Ukrainian specialist teams fixed one of two damaged lines and would now be able to deliver all required off-site power to the power plant.

The power station in Chornobyl, which suffered a nuclear meltdown in 1986, is currently controlled by Russian troops.

Energy Minister Herman Halushchenko said that "heroes" from the national power grid company managed to repair the connection, according to the AP report. That means the cooling systems that work to prevent radiation leaks are operating normally.

— Yun Li

Red Cross warns of 'worst-case scenario' for civilians in Mariupol

The hundreds of thousands of Ukrainians still in Mariupol are facing the "worst-case scenario" unless leaders are able to reach a "concrete humanitarian agreement urgently," the International Committee of the Red Cross warned.

Conditions in the heavily besieged port city are dire, with the Red Cross agency detailing shortages of food, water and medicine. People are risking their lives to find basic necessities and sheltering in unheated basements, it added.

"We call on all parties involved in the fighting to place humanitarian imperatives first. People in Mariupol have endured a weekslong life-and-death nightmare. This needs to stop now. Their safety and their access to food, water and shelter must be guaranteed," Peter Maurer, ICRC president, said in a statement.

Russia and Ukraine have agreed to partial cease-fires to allow civilians to leave the city, but multiple reports indicate attacks continued after the set time. That's led Ukrainian leaders to accuse Moscow of refusing to let civilians out of the city.

—Jessica Bursztynsky

Many Ukrainians find refuge underground in the Kharkiv Metro

For those who remain in Kharkiv, a city in northeast Ukraine, many have taken refuge underground in the city's Metro stations.

— Adam Jeffery

Zelenskyy calls on software giants to stop support services in Russia

Ukrainian President Volodymyr Zelenskyy called on software giants Oracle, Microsoft and SAP to stop support services for their products in Russia.

"Now can be no 'half' decisions or 'halftones'! There is only black and white, good or evil! You are either for peace or support the bloody Russian aggressor to kill Ukrainian children and women," Zelenskky wrote on Twitter.

"Stop supporting your products in Russia, stop the war!" he added.

Ukrainian officials have been pressuring technology giants and corporations still doing business in Russia to pull their products and support from the country.

— Jessica Bursztynsky

U.S. journalist and filmmaker Brent Renaud killed in Ukraine

American journalist and filmmaker Brent Renaud was killed by Russian forces on Sunday in Ukraine, a State Department spokesman confirmed.

"We offer our sincerest condolences to his family on their loss and are offering all possible consular assistance. Out of respect for his family's privacy, we have no specifics to offer at this time," the spokesman.

Renaud was a Peabody Award-winning documentary filmmaker, television producer and journalist, who lived and worked in New York City and Little Rock, Ark., according to his biography on the Renaud Brothers website.

He worked with his brother Craig on a number of film and TV projects covering the wars in Iraq and Afghanistan, the earthquake in Haiti and political turmoil in Egypt and Libya, according to the website.

Renaud was also a contributor to the New York Times.

"We are deeply saddened to hear of Brent Renaud's death. Brent was a talented filmmaker who had contributed to The New York Times over the years," The New York Times said in a statement. "Though he had contributed to The Times in the past (most recently in 2015), he was not on assignment for any desk at The Times in Ukraine. Early reports that he worked for Times circulated because he was wearing a Times press badge that had been issued for an assignment many years ago."

— Yun Li

IMF's Georgieva says Russian sovereign default no longer improbable

International Monetary Fund Managing Director Kristalina Georgieva said a Russian sovereign default could happen.

"In terms of servicing debt obligations, I can say that no longer we think of Russian default as [an] improbable event," Georgieva said on CBS's "Face the Nation" on Sunday. "Russia has the money to service its debt, but cannot access it."

The country, whose Ukraine invasion has entered its third week, is facing those economic consequences amid massive sanctions by the U.S. and other allies.

Last week, rating agency Fitch downgraded Russia's sovereign rating by six notches further into junk territory to a C grade, saying a default is "imminent."

Moody's and S&P have also slashed the country's sovereign rating to "junk" status, saying Western sanctions could undermine Russia's ability to service its debt.

— Yun Li

Evacuation train hit by shelling, conductor killed

An evacuation train in eastern Ukraine came under fire, killing the conductor and injuring another individual, the country's national railroad Ukrzaliznytsia said in a statement. It marks the latest attack against civilians who are attempting to escape violence.

It wasn't immediately clear how many people were on the train. The railroad company was working to evacuate the crew and passengers on the train, which includes about 100 children, it said.

The train was on its way to pick up evacuees from Lyman. It had been near the Brusyn station in the Donetsk region when it was hit by shelling, the company said in a Facebook post.

Ultimately, the train was headed to Lviv, a city in the Western part of Ukraine that many refugees have seen as a transfer point to get to safety, Ukrainian official Pavlo Kyrylenko said in a Telegram post.

"The occupiers crossed all possible boundaries of common sense and humanity," Kyrylenko said. "They must receive proper punishment for their hellish crimes!"

—Jessica Bursztynsky

UN says at least 596 dead in Ukraine

At least 596 people, including 43 children, have been killed since Russia began its invasion on Ukraine, the United Nations said. An additional 1,067 civilians, including 57 children, were wounded as of midnight on Saturday.

U.N. officials have said they believe actual casualties are "considerably higher," as reports in some areas are delayed and others are pending confirmation.

Most of the casualties have been caused by the use of explosive weapons that have a "wide impact area," including shelling from heavy artillery and multi-launch rocket systems, missiles and airstrikes, the agency said.

The death toll has continued to rapidly mount since troops invaded on Feb. 24, while Ukrainians still are trying to flee the country. U.S. officials have said they are collecting evidence of possible war crimes, human rights abuses and violations of international law by Russia.

"What we've been seeing in recent three weeks is a series of deliberately committed war crimes, crimes against humanity," Ukrainian Foreign Minister Dmytro Kuleba said Sunday of civilian deaths on CBS's "Face the Nation with Margaret Brennan." "And when they bomb hospitals, maternity houses, schools, when they kill civilians passing by trying to be evacuated from the war zone, that, of course, indicates that they are trying to break us down and to destroy us."

—Jessica Bursztynsky

A second mayor captured by Russian forces, Ukrainian official says

A second Ukrainian mayor was abducted by Russian forces on Sunday according to Dmytro Kuleba, the nation's top diplomat.

"Today, Russian war criminals abducted another democratically elected Ukrainian mayor, head of Dniprorudne Yevhen Matveyev," Kuleba wrote on Twitter. 

Yevhen Matveyev, the mayor of Dniprorudne, a southern port city in Ukraine, is the second known mayor to be captured by Russian forces. Ukrainian officials said the mayor of the southeastern city of Melitopol, Ivan Fedorov, was captured by Russian soldiers on Saturday.

Ukrainian President Volodymyr Zelenskyy wrote in a tweet on Saturday that he spoke with French President Emmanuel Macron and German Chancellor Olaf Scholz for help in the release of Fedorov.

— Amanda Macias

Zelenskyy meets with wounded troops at hospital

Ukrainian President Volodymyr Zelenskyy visited a hospital to meet with wounded service members fighting against Russian forces.

In the three-minute video, which was posted on Telegram, Zelenskyy is seen at the bedside of wounded troops, shaking hands and posing for selfies. He also appears to award one soldier with a medal.

— Amanda Macias

'Arm Ukraine and we will do the rest,' Ukrainian official says

Ukrainian Foreign Minister Dmytro Kuleba called on allies and partners to continue to supply his country with more firepower, as the Kremlin's war approaches the fourth week.

Kuleba also said he does not expect NATO allies to defend Ukraine in the event of a potential chemical attack. Instead, he called on the alliance to deploy more weapons and defensive systems.

"We say arm Ukraine and we will do the rest. Give us all the weapons necessary and we will fight for our own land and for our people, Kuleba told CBS Sunday program "Face the Nation with Margaret Brennan."

He added that "the most pressing issue" is to equip the Ukrainian Air Force with more planes.

He described Ukraine's air power as "uncomparable" to Russia's fleet. Last week, the Pentagon scrapped a plan to send Russian-made MiG-29 fighter jets to Ukraine citing logistics issues of flying aircraft into contested airspace.

— Amanda Macias

Military Chaplain Nikolay Medynsky blesses Ukrainian soldiers in Kyiv

Military Chaplain Nikolay Medynsky blesses Ukrainian soldiers in Kyiv as Russia's attack on the Ukraine continues.

-Adam Jeffery

Instagram service will cease at midnight in Russia

Russian Instagram users were alerted that the Meta-owned platform will cease operations in the country starting at midnight.

The state communications regulator sent an email encouraging people to move their photos and videos from Instagram before it was shut down and to switch to Russia's own "competitive internet platforms," Reuters reported.

Instagram chief Adam Mosseri has said the decision would cut 80 million users in Russia off from one another.

The decision comes after Meta began allowing users in Ukraine to call for violence against Russia's president and military. Russia opened a criminal case against the company, attempting to have it declared an extremist organization because of the temporary change in its hate speech policy to permit threats on Instagram and Facebook in the context of Russia's Ukraine invasion.

Russia's media regulator has already blocked Meta's flagship app Facebook in the country.

—Jessica Bursztynsky

Jake Sullivan and China’s Yang Jiechi to discuss Ukraine on Monday

National security adviser Jake Sullivan will meet in Rome on Monday with China's top diplomat, Yang Jiechi, to discuss the Kremlin's war in Ukraine.

The meeting, which will include officials from the National Security Council and State Department, follows warnings from Washington that Beijing should not alleviate the economic pressure mounting on Moscow.

"The two sides will discuss ongoing efforts to manage the competition between our two countries and discuss the impact of Russia's war against Ukraine on regional and global security," the White House said in a statement.

Sullivan told CNN's Dana Bash in a Sunday interview that "there will absolutely be consequences for large scale sanctions evasion efforts or support to Russia to backfill them."

"We will not allow that to go forward and allow there to be a lifeline to Russia from these economic sanctions from any country anywhere in the world," he added.

Sullivan will also meet with Luigi Mattiolo, a diplomatic advisor to Italy's prime minister, on "coordinating a strong, united international response to President Putin's war of choice."

— Amanda Macias

Pentagon is sending more firepower to Ukraine

The Pentagon is working to send additional military equipment to Ukraine as part of President Joe Biden's weekend authorization of an additional $200 million.

"We're going to get working on that right away to get that additional material into their hands," Pentagon spokesman John Kirby told ABC News on Sunday.

Kirby declined to specify what type of U.S. military equipment could be forward deployed to Ukraine but said that the most effective platforms are air defense systems, drones and man-portable air-defense systems or MANPADS.

"They are doing very well with that and we believe those are what they need the most," Kirby added.

— Amanda Macias

Anti-war protesters arrested in St. Petersburg and Moscow, Russia

Russian police arrested numerous anti-war protesters in St. Petersburg and Moscow as the Russian invasion of Ukraine continues.

-Adam Jeffery

Sullivan warns of potential miscalculations amid Putin’s provocative rhetoric on nuclear weapons

National security advisor Jake Sullivan condemned Russian President Vladimir Putin's rhetoric around Moscow's nuclear posture and warned of potential miscalculations.

Last month, Putin placed his nation's nuclear forces on high alert amid tensions with the West over the invasion of Ukraine. Putin, speaking in a meeting on Feb. 27 with his top defense officials, cited "aggressive statements" made against Russia by NATO as a reason to order the elevation.

"We are watching this extremely closely and obviously the escalation risk with nuclear power is severe and it is a different kind of conflict," Sullivan told CNN's Dana Bash when asked if Putin would use a nuclear weapon.

Of the world's combined nuclear weapons inventory, Washington and Moscow own the lion's share with approximately 4,000 warheads each.

Sullivan added that the U.S. has not adjusted its nuclear weapons posture but that the administration is monitoring this issue "day by day, hour by hour because it is a paramount priority to the president."

— Amanda Macias

White House watching China closely as Putin attempts to blunt sweeping sanctions

The Biden administration said it is watching to see if the world's second-largest economy comes to the aid of Russian President Vladimir Putin amid a slew of punishing sanctions.

National security advisor Jake Sullivan said the U.S. believes China was aware of Putin's pre-planned invasion of Ukraine.

"They [China] may not have understood the full extent of it because it's very possible that Putin lied to them the same way that he lied to Europeans and others," Sullivan told CNN's Dana Bash.

"We also are watching closely to see the extent to which China actually does provide any form of support, material support or economic support to Russia. It is a concern of ours and we have communicated to Beijing that we will not stand by and allow any country to compensate Russia for its losses," he added.

— Amanda Macias

'Vladimir Putin does not look like he is prepared to stop the onslaught,' Biden security advisor says

National security advisor Jake Sullivan said Sunday that Russian President Vladimir Putin "does not look like he is prepared to stop the onslaught" in Ukraine.

Sullivan told CNN's Sunday program that while the United States will not send troops to fight in Ukraine, the Biden administration will "escalate the pressure against him [Putin] and continue to support the Ukrainians."

Sullivan added that the U.S. was coordinating with NATO allies on sending additional military and humanitarian aid to Ukraine.

— Amanda Macias

With nearly half its gold and currency reserves frozen, Russia turns to China

Russia said it is counting on China to assist it as Western sanctions batter its economy, Reuters reported. The sanctions have frozen nearly half of the country's gold and foreign currency reserves.

"We have part of our gold and foreign exchange reserves in the Chinese currency, in yuan. And we see what pressure is being exerted by Western countries on China in order to limit mutual trade with China. Of course, there is pressure to limit access to those reserves," Finance Minister Anton Siluanov said.

"But I think that our partnership with China will still allow us to maintain the cooperation that we have achieved, and not only maintain, but also increase it in an environment where Western markets are closing."

Siluanov made the remarks in a TV interview, Reuters said, and made it clear that Moscow is reaching out to China to help cushion the blow on its economy.

— Terri Cullen

Pope Francis says 'unacceptable armed aggression' in Ukraine must stop

Pope Francis has issued a strong condemnation of the war in Ukraine, saying the "unacceptable armed aggression" must stop before it reduces cities to cemeteries.

"In the name of God, let the cries of those who suffer be heard and let the bombings and attacks cease," Pope Francis said during his Sunday blessing, addressing thousands of people in St. Peter's Square in Rome.

"Let there be a real and decisive focus on negotiation, and let the humanitarian corridors be effective and safe. In the name of God, I ask you: stop this massacre," he said, describing the killing of children and unarmed civilians as "barbaric."

— Holly Ellyatt

U.K. considers using sanctioned oligarchs' properties for refugees

Britain is exploring whether it can use properties belonging to sanctioned Russian oligarchs for humanitarian purposes.

Housing Secretary Michael Gove said Sunday that seized homes in Britain could potentially be used to house refugees from Ukraine as the government seeks to improve its response to the migrant crisis following heavy criticism.

"I want to explore an option which would allow us to use the homes and properties of sanctioned individuals for as long as they are sanctioned for humanitarian and other purposes," Gove told the BBC.

Given that the sanctioned properties have not been permanently confiscated, Gove noted that the legal barriers of such a move could be high. However, he added, "if we can use [the properties] in order to help others, let's do that."

— Karen Gilchrist

Death toll rises after Russia strikes Ukrainian military facility

At least 35 people have been killed and 134 injured after Russia attacked a military training base in western Ukraine, the Lviv regional governor said on Sunday.

The death toll has risen from an earlier tally that stated there had been nine fatalities and 57 people wounded in the attack on the International Peacekeeping and Security Centre (IPSC), in Ukraine's Yavoriv district.

That location of the military facility, which is used for training Ukraine's armed forces, is around 32 miles (52 km) from the major western Ukrainian city of Lviv.

— Holly Ellyatt

Any use of chemical weapons by Russia would be a 'game changer,' Poland's president says

Poland's President Andrzej Duda said in an interview on Sunday that the use of chemical weapons in Ukraine by Russia would be a "game changer" and a red line for NATO.

"If he uses any weapons of mass destruction then this will be a game changer in the whole thing," he told the BBC's Sophie Raworth on Sunday, adding that NATO would have to "think seriously what to do because then it starts to be dangerous."

With his almost universally condemned invasion of Ukraine, which began on Feb.24, Russian President Vladimir Putin is seen as an increasingly unpredictable leader.

As Russia is facing far more resistance than it expected in Ukraine, and appearing to prepare to attack the capital Kyiv, there are fears that Putin could resort to using unconventional — and outlawed — weapons.

— Holly Ellyatt

Nine reportedly killed and 57 wounded in Russian strike on military facility

Nine people have been killed and 57 wounded in an air strike on a military facility in western Ukraine, according to a Reuters report citing the governor of the Lviv region, where the facility is located.

Russia targeted the military training center in western Ukraine, close to the border with Poland, earlier on Saturday. Lviv's regional military administration said that eight missiles were fired at the International Peacekeeping and Security Centre (IPSC), in Ukraine's Yavoriv district. That location is around 34 miles (55 km) from the major western Ukrainian city of Lviv.

A ministry representative told Reuters the ministry was still trying to establish if any of the instructors were at the centre at the time of the attack.

"Russia has attacked the International Center for Peacekeeping & Security near Lviv. Foreign instructors work here. Information about the victims is being clarified," Reznikov said in an online post, Reuters reported.

— Holly Ellyatt

U.K. warns Russian forces are trying to envelop Ukrainian forces in the east

The U.K.'s Ministry of Defense said Sunday that Russian forces are attempting to envelop Ukrainian forces in the east of the country.

The authorities said that military personnel are seen advancing from Kharkiv in the north and Mariupol in the south.

Additional Russian forces advancing from Crimea are trying to circumvent Mykolaiv in the south as they attempt to drive west toward Odesa, the ministry said in a tweet.

"Russia is paying a high price for each advance as the Ukrainian Armed Forces continues to offer staunch resistance across the country," it said.

— Karen Gilchrist

Russia targets military site in western Ukraine, near Polish border

Russia has targeted a military training center in western Ukraine, close to the border with Poland, according to Ukrainian authorities.

Lviv's regional military administration said that eight missiles were fired at the International Peacekeeping and Security Centre (IPSC), in Ukraine's Yavoriv district.

That location is around 34 miles (55 km) from Lviv, a major city in the west of Ukraine where thousands of civilians have fled to or passed through as they try to get to Poland.

The IPSC is a training center for the Ukrainian army, particularly for peacekeeping missions. Information about any casualties is being established, the administration said.

At the start of Russia's invasion of Ukraine, its forces attacked predominantly in the north, east and south of the country, but in recent days Moscow has expanded its attacks to sites in the center and west.

— Holly Ellyatt

NATO secretary general warns that Russia may use chemical weapons

NATO Secretary General Jens Stoltenberg warned on Sunday that Russia might use chemical weapons against Ukrainians, Reuters reported, citing an interview with a German newspaper.

Stoltenberg told Welt am Sonntag that such an attack would constitute a war crime, but that Russia appeared to be inventing advance justification for using chemical weapons.

"In recent days, we have heard absurd claims about chemical and biological weapons laboratories," said Stoltenberg, who added that the Kremlin was creating a false pretext to justify something that can't be justified.

— Ted Kemp

Russia wants to break Ukraine into 'pseudo-republics,' Zelenskyy says

Ukraine President Volodymyr Zelenskyy said in a nightly address that Russia is trying to break up the country by creating new "pseudo-republics," the Associated Press reported.

"The occupiers on the territory of the Kherson region are trying to repeat the sad experience of the formation of pseudo-republics," Zelenskyy said, according to AP. "They are blackmailing local leaders, putting pressure on deputies, looking for someone to bribe."

Zelenskyy said that Kherson city council members on Saturday rejected plans for a new republic. Kherson is in Ukraine's south and now under the control of Russian forces.

Before invading Ukraine in late February, Russia "recognized" the Ukrainian regions of Donetsk and Luhansk as new, independent countries.

Russia has supported a separatist war in the east of Ukraine since 2014.

— Ted Kemp