Dozens of Iraqi Shiite militiamen and their supporters have broken into the US Embassy in Baghdad, setting fire to a reception area, as protests over US airstrikes targeting an Iran-backed militia turned violent.

Key points: The US ambassador to Iraq and other staff were evacuated for their safety

The US ambassador to Iraq and other staff were evacuated for their safety Tear gas was fired in an attempt to disperse the protesters outside the embassy

Tear gas was fired in an attempt to disperse the protesters outside the embassy The militias encouraged protesters through loudspeakers to leave to "avoid bloodshed"

Protests outside the embassy began on Monday (local time) after the US strikes against the Kataib Hezbollah militia group killed at least 25 fighters.

The US claimed it was in response to the killing of a US civilian contractor in a rocket attack on an Iraqi military base.

President Donald Trump blamed Iran for the embassy breach and called on Iraq to protect the diplomatic mission.

"Iran killed an American contractor, wounding many. We strongly responded, and always will. Now Iran is orchestrating an attack on the US 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!" he tweeted from his estate in Palm Beach, Florida.

The US is expected to temporarily send additional Marines to its embassy, according to officials, who spoke on the condition of anonymity.

Protesters threw stones at the embassy gate and started fires next to the walls, while chanting "No, no America!" and "No, no Trump!"

Iraqi special forces were deployed around the main gate to try and prevent protesters from entering, firing tear gas in an attempt to disperse the crowd.

Some of the militias encouraged protesters through loudspeakers to leave.

"We have delivered our message, please leave the area to avoid bloodshed," one announcement said.

The US State Department and White House did not immediately respond to a request for comment on whether the US ambassador and other staff had been evacuated from the embassy compound in the Iraqi capital.

However, Iraqi officials said the ambassador and other staff were evacuated from the embassy for their safety.

'Americans are unwanted in Iraq'

Iraqis have been taking to the streets in their thousands almost daily to condemn, among other things, militias such as Kataib Hezbollah and their Iranian patrons that support Iraqi Prime Minister Adel Abdul Mahdi's government.

But on Tuesday, it was these militias who were spraying "Closed in the name of the people" on the gates of the US Embassy and smashing the surveillance cameras around the building with bricks and stones.

Qais al-Khazali, leader of the Iranian-backed Asaib Ahl al-Haq militia, and many other senior militia leaders were among the protesters.

Protesters and militia fighters gather outside the main gate of the US embassy. ( Reuters: Thaier al-Sudani )

"Americans are unwanted in Iraq," said Mr Khazali, one of the most feared and respected Shiite militia leaders in Iraq, and one of Iran's most important allies.

"They are a source of evil and we want them to leave."

Kataib Hezbollah is one of the smallest but most potent Iranian-backed militias. Its flags were hung on the fence surrounding the embassy.

Militia commander Jamal Jaafar Ibrahimi, also known as Abu Mahdi al-Mohandes, and Badr Organisation leader Hadi al-Amiri were also at the protest.

Mr al-Mohandes has condemned the air strikes, which killed at least 25 fighters and wounded 55.

Reuters