• The drone attack, which also injured at least 34 U.S. personnel, marks the first deaths of U.S. troops by enemy fire since Oct. 7.
• "Hit Iran now. Hit them hard," Republican Sen. Lindsey Graham said in a statement.
• Biden vowed to retaliate, saying in a statement that "we will hold all those responsible to account at a time and in a manner our choosing."

Congressional lawmakers are demanding President Joe Biden strike Iran after three U.S. troops were killed Sunday night in Jordan in a drone strike claimed by the Islamic Resistance in Iraq, an Iranian-backed militia group.

The deadly drone attack, which also injured at least 34 U.S. personnel, marks the first deaths of U.S. troops by enemy fire since the latest Israel-Hamas war began after Palestinian militant group Hamas' Oct. 7 terror attack on Israel. Iran has denied involvement in the strike, while Jordan's government denied it took place on its soil.

"I am calling on the Biden Administration to strike targets of significance inside Iran, not only as reprisal for the killing of our forces, but as deterrence against future aggression," Republican Sen. Lindsey Graham of South Carolina said in a statement.

"The only thing the Iranian regime understands is force. Until they pay a price with their infrastructure and their personnel, the attacks on U.S. troops will continue," he added. "Hit Iran now. Hit them hard."

Roger Wicker of Mississippi, the most senior Republican on the Senate Armed Services Committee, said: "We must respond to these repeated attacks by Iran and its proxies by striking directly against Iranian targets and its leadership. ... The Biden administration's responses thus far have only invited more attacks." 

Biden for his part vowed to retaliate, saying in a statement that "we will hold all those responsible to account at a time and in a manner our choosing."

The attack marks another regional escalation in a war that the Biden administration has tried to contain.

Already, conflict has spilled over into the Red Sea, with Yemeni Houthi rebels attacking ships in protest of the Israeli bombardment of Gaza and Israel's U.S. backer. The U.S. and U.K. have launched airstrikes against Houthi positions in Yemen, but so far have failed to deter the group's activities.

Meanwhile, Lebanese Shia militia group Hezbollah and Israel are exchanging fire along the Israeli-Lebanese border, while Iran earlier this month struck targets in Iraq, Syria and Pakistan. Only the Iraqi target was purportedly linked to Israel, but Tehran's recent assertiveness is likely a signal to the U.S. and Israel about its capabilities. Both Hezbollah and the Houthis are supported by Iran.

Despite this, numerous regional analysts warn that Iran does not necessarily have full control over the actions of the proxy groups that it arms around the Middle East.

"Unlike Lebanese Hezbollah, which has been more measured in its response to the Gaza war, the Iraqi militias and the Houthis have displayed a high tolerance for direct confrontation with the United States," Helima Croft, head of global commodity strategy and MENA research at RBC Capital Markets, wrote in an analysis note.

The risk of wider conflict and deeper U.S. involvement led oil prices to jump Monday morning. Both Washington and Tehran have expressed their desire to avoid more kinetic involvement in the war, likely understanding the sheer scale of destruction a direct confrontation between the two adversaries would cause.

"Striking Iran directly would be extremely costly, extremely risky for the U.S.," Dominic Pratt, a senior country analyst for the Middle East and Africa at the Economist Intelligence Unit, told CNBC. Short of that approach, he said, would be for the U.S. to continue on its current path of attacking Iranian proxy groups in Syria, Iraq and Yemen, as well as expanding financial pressures like sanctions.

But that has clearly failed to deter the latest attacks on U.S. personnel in the region — there have been at least 160 attacks by Iran-backed groups on Middle Eastern bases where Americans are present during the more than 3½ months since the Israel-Hamas war began.

"As long as the war in Gaza continues, we're likely to see these attacks carry on," Pratt said.

"A lot of these groups have tied their attacks directly to Israel's war against Hamas in Gaza and the U.S. support for it. ... So for as long as this this war continues, we'll continue to see an escalation of these attacks, or at least that these attacks will carry on as they are, which broadens the risk that there will be an escalation like what we've seen with the attack on the base in Jordan."