President Trump accused Iran of orchestrating the attack at the U.S. Embassy compound in Iraq on Tuesday and vowed to hold the regime "fully responsible."

Dozens of Iraqi Shiite militia supporters had gained entry to the compound in Baghdad after reportedly smashing down a gate and storming inside. It came amid protests over U.S. airstrikes, though Trump stressed that the strikes were in response to the killing of an American contractor.

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"Iran killed an American contractor, wounding many. We strongly responded, and always will," Trump tweeted Tuesday morning. "Now Iran is orchestrating an attack on the U.S. Embassy in Iraq. They will be held fully responsible. In addition, we expect Iraq to use its forces to protect the Embassy, and so notified!"

The breach at the compound followed an earlier attempt by hundreds of Iraqis. The unrest came as Iraqis held funerals for the 25 fighters from Iran-backed Shiite militia Kataeb Hezbollah who were killed in U.S. airstrikes earlier this week, the Associated Press reported. The U.S. military said the airstrikes were in retaliation for last week's killing of an American contractor in a rocket attack on an Iraqi military base that it had blamed on the militia.

Reporters for the AP described a chaotic scene on the ground Tuesday and said the crowd shouted, “Down, down USA!” An AP reporter at the scene saw flames rising from inside the compound and at least three U.S. soldiers on the roof of the embassy.

There were no reports of casualties, but the unprecedented breach was one of the worst attacks on the embassy in recent memory. Iraq has long struggled to balance its ties with the U.S. and Iran, both allies of the Iraqi government. But the government's angry reaction to the U.S. airstrikes and its apparent decision not to prevent the protesters from reaching the embassy signaled a sharp deterioration of U.S.-Iraq relations.

Iraqi security forces made no effort to stop the protesters as they marched to the heavily fortified Green Zone. A man on a loudspeaker later urged the mob not to enter the compound, saying: "The message was delivered."

Two Iraqi foreign ministry officials initially told Reuters the U.S. ambassador and staff were evacuated, but U.S. officials pushed back, telling Fox News that the embassy has not been evacuated. Further, an official said Ambassador Matthew H. Tueller was not evacuated but has been out of the country on a previously planned vacation.

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U.S. lawmakers similarly blamed Iran for the embassy assault, with Sen. Marco Rubio, R-Fla., tweeting that they were "directly responsible for orchestrating" it.

"When an Iran-backed militia killed an American in Iraq last week, it met with a firm response. Now our embassy in Baghdad—sovereign U.S. territory—has been attacked in yet another reckless escalation. As the President notes, Iran must be held responsible," Sen. Tom Cotton, R-Ark., tweeted.

Fox News' Lucas Tomlinson, Edmund DeMarche and Jack Durschlag and The Associated Press contributed to this report.