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.