Protesters angered by recent deadly US air strikes targeting an Iranian-backed Iraqi militia have attacked the US embassy compound in Baghdad. US troops fired tear gas to disperse a crowd that breached the outer wall of the compound, which is in the capital's heavily fortified Green Zone. A guard post on the street nearby was also set alight. US President Donald Trump accused Iran of "orchestrating" the attack and said it would be "held fully responsible". At least 25 fighters died when the US bombed bases associated with the Kataib Hezbollah militia in western Iraq and eastern Syria on Sunday. The US said it was retaliating for a rocket attack on an Iraqi military base in Kirkuk on Friday that killed an American civilian contractor. Iraqi Prime Minister Adel Abdul Mahdi said on Monday that the strikes had violated his country's sovereignty and would force it to review its relations with the US. Kataib Hezbollah's commander, Abu Mahdi al-Muhandis, warned that the militia's response "would be very tough on the American forces in Iraq". Iran described the attacks as a "clear example of terrorism". Tuesday's protest took place after funerals were held in Baghdad for the militia fighters who were killed in the US strikes. Thousands of mourners - including Abu Mahdi al-Muhandis and several other senior militia and paramilitary leaders - marched towards the Green Zone, where many Iraqi government offices and foreign embassies are located. They were allowed by Iraqi security forces to enter the zone and gather on a street outside the US embassy compound. Waving Kataib Hezbollah and other militia flags, and chanting anti-American slogans, the protesters threw stones at the compound's main gate, pulled down security cameras, attacked empty guard posts, and started several fires. The situation later escalated when the compound's wall was breached. The Associated Press reported that a gate used by cars was smashed open and that dozens of people pushed about 5m (16ft) into a corridor leading to the main embassy building before being forced to retreat by tear gas fired by US troops. Iraqi soldiers and riot police were reportedly later deployed in the area, and Prime Minister Abdul Mahdi told the protesters to leave the compound immediately. "Any aggression or harassment of foreign embassies will be firmly prohibited by the security forces," Mr Abdul Mahdi added. The Popular Mobilisation, a paramilitary force dominated by Iran-backed Shia militias, reported that 20 protesters were wounded by live rounds and tear-gas canisters. Kataib Hezbollah meanwhile called for protest in front of the embassy until it was closed and the ambassador was expelled from Iraq, the website Al-Sumaria said. President Trump tweeted: "Iran killed an American contractor, wounding many. We strongly responded, and always will. 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!" There was no immediate response from the Iranian government. It was not clear whether civilian staff were inside the embassy during the attack. There were reports that the US ambassador, Matthew Tueller, had been evacuated. But a source close to the embassy told the BBC that Mr Tueller had left the country before Sunday's strikes for a planned Christmas holiday.