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Thousands of Iraqi supporters of the largely Iranian-trained PMF fighters had encircled and vandalised the embassy compound Tuesday, outraged by US air strikes that killed 25 Hashd fighters over the weekend.

They marched unimpeded through the checkpoints of the usually high-security Green Zone to the embassy gates, where they broke through a reception area, chanting "Death to America" and spraying pro-Iran graffiti on the walls.

Iraq's caretaker premier Adel Abdel Mahdi called on the angry crowd to leave the embassy but most spent the night in dozens of tents set up outside the perimeter wall.

On Wednesday morning, crowds of men brandished the paramilitary force's colours, torched US flags and hurled rocks towards the compound. 

Security personnel inside responded with tear gas, wounding at least 20 people, the PMF said. 

By the afternoon, the PMF called on its supporters to leave the embassy and regroup outside the Green Zone "out of respect for the state". 

"You delivered your message," it said in a statement. 

AFP's photographer saw protesters dismantle their tents and leave the Green Zone, screaming "We burned them!".

Minister of Interior Yassin al-Yasiri, a Shia politician, was in front of the US Embassy overseeing the withdrawal of militia protesters, according to Iraqi .

Hezbollah Brigades, the group targeted in the US raids, initially told AFP it would stay at the embassy.

But the group's spokesman Mohammad Mohyeddin later said it had decided to abide by the PMF's order.

"We scored a huge win: we arrived to the US embassy, which no one had done before," he told AFP.

"Now, the ball is in parliament's court," Moyheddin added, referring to lawmakers' efforts to revoke the legal cover for 5,200 US troops to deploy in Iraq. 

'You can't do a thing'

Tuesday's embassy attack was the latest episode in spiralling tensions between the United States and Iran since Washington abandoned a landmark nuclear deal with Tehran in 2018.

Many of those tensions have played out in Iraq, which has close ties with both governments.

US forces have faced a spate of rocket attacks in recent months, blaming them on pro-Iran Hashd factions.

Last week, one of those attacks killed a US contractor, prompting the retaliatory US air strikes that killed 25 fighters from Hezbollah Brigades.

President Donald Trump and other US officials have blamed Iran for attacks on US forces and the embassy. 

"They will pay a very BIG PRICE! This is not a Warning, it is a Threat," Trump wrote on Twitter, adding "Happy New Year!"

Read more: Trump sets 'red line' for Tehran amid mounting risks

Iran's supreme leader Wednesday condemned US strikes on Iraq and warned his country was ready to hit back.

"First of all, you can't do a damn thing! This has nothing to do with Iran," Ayatollah Ali Khamenei said in a speech on state television.

"If the Islamic republic decides to oppose or fight against a country, it will do this explicitly," he said.

Tehran's foreign ministry said it had summoned an official from the Swiss embassy, which represents US interests in Iran, over American "warmongering" in Iraq.

'Our hands are tied'

By Wednesday, Iraqi forces had reimposed normal security measures around the perimeter of the Green Zone, usually inaccessible without a badge.

US officials were alarmed that protesters crossed checkpoints so easily on Tuesday.

An Iraqi special forces fighter assigned to guard the Green Zone told AFP his units had no orders to intervene.

"If I had had orders to act, I could have fired and stopped the storming of the embassy," he said.

"But after what happened, our hands are tied. We can't prevent the situation from deteriorating," he added.

US officials have pressured Iraqi authorities to step up security and sent a rapid response team of marines overnight to help guard the compound.

US Defence Secretary Mark Esper said around 750 troops from the 82nd Airborne Division were prepared to deploy to the region in the coming days.

No US personnel were injured in the attack and US officials said they had no plans to evacuate.

Ambassador Matthew Tueller was said to be on his way back to Baghdad from holiday but had yet to arrive on Wednesday afternoon.

Read also: Protests bring Iraq’s muhasasa system to its knees

The attack highlighted new strains in the US-Iraqi relationship, which officials from both countries have described to AFP as the "coldest" in years.

The US led the 2003 invasion against then-dictator Saddam Hussein and has worked closely with Iraqi officials since, but its influence has waned compared with Tehran's growing clout.

Tuesday's dramatic scenes at the embassy sparked comparisons with both the 1979 hostage crisis at the US embassy in Tehran and the deadly 2012 attack on the US consulate in Libya's second city Benghazi.