Sen. Lindsey Graham (R-S.C.) warned Thursday of an "aggressive" response to a rocket strike in Iraq that killed two U.S. service members that officials are blaming on an Iran-backed militia.

"I think the president's going to be very aggressive," said Graham, a top GOP defense voice and close ally of President Trump's. "At the time of our choosing, we should hit back."

Asked if he meant retaliation against the militia or Iran itself, Graham said, "the people who actually launched the rockets."

"Put Iran on notice that we're going to hold them accountable in the future for this," Graham added.

Senate Foreign Relations Committee Chairman Jim Risch (R-Idaho) also warned that "if I was the Iran proxy group, I would not sleep well tonight."

On Wednesday night, U.S. military officials said 18 Katyusha rockets hit Camp Taji, a base north of Baghdad. The attack killed three - the two Americans and a British service member - and wounded 12. Iraqi forces found a rocket-rigged truck a few miles from Camp Taji, the U.S.-led coalition in Iraq added.

On Thursday, Defense Secretary Mark Esper attributed the attack to Iranian-backed Shia militia groups and said that "all options are on the table" to respond.

"Let me be clear, the United States will not tolerate attacks against our people, our interests or our allies," Esper said.

The attack Wednesday had echoes of a similar rocket strike in December that set off an escalatory cycle that brought the United States and Iran to the brink of war.

In December, U.S. officials blamed the Iran-backed Kataib Hezbollah for a rocket attack that struck a base near Kirkuk, killing one U.S. contractor and wounding four U.S. service members.

The confrontation culminated with a U.S. drone strike that killed Iranian Gen. Qassem Soleimani, followed by an Iranian missile attack on bases in Iraq that gave more than 100 U.S. troops brain injuries.

Responding to Wednesday's rocket attack, Senate Armed Services Committee Chairman James Inhofe (R-Okla.) said the United States is "obviously" going to exact "reprisal," though he wouldn't specify what form he expects that to take.

U.S. officials have touted the Soleimani strike as having "reestablished deterrence" against Iran.

Democrats, who were skeptical of that argument to begin with, are pointing to Wednesday night's attack as belying the deterrence line.

"Clearly we didn't restore deterrence," Sen. Chris Murphy (D-Conn.) said. "That was a lie. The Iranians are still shooting at us."

Murphy the United States should "start talking to the Iranians" after Wednesday's attack.

"It is so frightening that this escalatory continues and we have no mechanism to talk to the Iranians," he said. "If we can't begin a direct dialogue with the Iranians then there's no hope of there being any permanent deescalation."

He added that the Trump administration backed itself into a corner by drawing a red line against Americans being killed.

"If that red line exists, then obviously they would be contemplating retaliatory action," he said. "I don't think that would be a good idea. But I also don't understand what the administration's policy is if they choose not to respond."

Last month, the Senate passed a resolution aimed at blocking Trump from taking military action against Iran in response to the Soleimani strike and subsequent spike in tensions. The House passed the measure, sending it to Trump's desk on Wednesday as news was breaking about the latest rocket attack.

Trump has threatened to veto the measure, and neither chamber of Congress is expected to have the votes to override the veto.

Sen. Tim Kaine (D-Va.), who sponsored the resolution, said it is within Trump's authority to protect U.S. troops from Iran-backed militia groups, noting his measure was specifically tailored to military action against the government of Iran.

"This attack yesterday is very troubling," Kaine said. "The president has the power that he needs to take action against militia groups."

Kaine also cast doubt on whether this strike would result in the same escalatory cycle as last time, citing internal pressures in Iran such as its massive coronavirus outbreak.

"I'm not expecting it to ramp up because I think the number of other pressures that Iran is under right now is going to have them focused inward," Kaine said. "But there's a countertheory that says that's when authoritarian nations do something to take their attention off their internal woes."