President Biden and other top U.S. officials discussed Sunday a "significant military response" against pro-Iranian militias over the drone attack near the Jordan-Syria border that killed three American soldiers and wounded dozens of others, a U.S. official and another source briefed on the matter told Axios.

Why it matters: The White House and Pentagon are hoping to calibrate their retaliation to contain the growing risk of regional war. But pressure for more significant action is brewing on Capitol Hill, with hawks pushing for strikes inside Iran.

The latest: The Pentagon on Monday identified the three American soldiers killed in the attack as Sgt. William Jerome Rivers, 46; Spc. Kennedy Ladon Sanders, 24; and Spc. Breonna Alexsondria Moffett, 23.

• More than 40 service members are estimated to have been injured in the attack, Pentagon Deputy Spokesperson Sabrina Singh said at a press briefing Monday, warning that the number may rise.

Driving the news: "We don't want war but those who are behind this attack need to feel our response," a U.S. official told Axios on Sunday evening.

• There have been more than 150 attacks targeting U.S. troops in the region since the Israel-Hamas war began on Oct. 7, many of them by pro-Iranian militias in Iraq and Syria. The attack in Jordan was the first to kill American soldiers.
• U.S. officials said Sunday that they were still working to determine exactly who launched the drone that hit the U.S. base, and whether it was launched from Iraq or Syria.
• Several more high-level meetings about the response took place Sunday in addition to the one Biden took part in, the sources said.
• "We shall respond," Biden vowed Sunday during an event in South Carolina, after requesting a moment of silence for the fallen soldiers.

What they're saying: While the Biden administration is preparing to hit Iran's proxies, Republican hawks are pushing Biden to hit Iran directly.

• Senate Minority leader Mitch McConnell (R-Ky.) called for "serious, crippling costs" to Iran, "not only on front-line terrorist proxies, but on their Iranian sponsors who wear American blood as a badge of honor."
• "The only answer to these attacks must be devastating military retaliation against Iran's terrorist forces, both in Iran and across the Middle East," said Sen. Tom Cotton (R-Ark.). "Anything less will confirm Joe Biden as a coward unworthy of being commander-in-chief."
• Sen. Lindsey Graham (R-S.C.) called on Biden to "strike targets of significance inside Iran."
• Sen. John Cornyn (R-Texas) tweeted "Target Tehran," later specifying that he was calling for strikes against Iran's Islamic Revolutionary Guard Corps.

Between the lines: While Biden's critics argue attacking Iran and its forces would inflict a much higher price than hitting proxies, the consequences would be more unpredictable and potentially far greater.

• Biden would also face an outcry from members of his own party, some of whom have rebuked him for not seeking congressional authorization for the strikes the U.S. has already conducted in recent weeks on Iran-backed groups in Iraq and Yemen.

Behind the scenes: The attack in Jordan took place as the White House was pushing for a hostage deal between Israel and Hamas that could lead to a two-month ceasefire in Gaza.

• CIA Director Bill Burns joined some of the consultations on Sunday from Paris, where he was meeting Qatar's prime minister and the Israeli and Egyptian spy chiefs to discuss the deal.
• Biden administration officials believe a ceasefire in Gaza is key to reducing regional tensions. During a previous one-week pause last November, attacks on U.S. forces in the region stopped almost completely.

The big picture: The war in Gaza has sent violent tremors through the region, with the U.S. becoming steadily more directly involved.

• A U.S. warship was forced to shoot down a missile launched at it by Houthi rebels in Yemen on Friday, while the Iran-backed rebels also struck a British ship.
• Houthi attacks near critical chokepoints like the Bab-el-Mandeb Strait have snarled international shipping. A U.S.-led initiative to police those waterways has brought more troops into the line of fire but thus far failed to restore calm.

Editor's note: This story has been updated with the names of the soldiers killed in the drone strike.