French Defence minister Florence Parly. Photo: AFP/Thomas Samson

French Defence Minister Florence Parly has condemned the attack on the US embassy in Baghdad by pro-Iranian demonstrators and expressed solidarity with France's coalition partner in a New Year's address to French troops.

"France strongly condemns the attacks carried out against the positions of the international coalition in Iraq and today's attempted incursion into the US embassy compound in Baghdad," Parly told the crew of the French frigate Courbet with whom she rang in the New Year.

In the speech, the text of which was only made public on Wednesday, she also expressed "full solidarity" with the US.

Supporters and members of the Popular Mobilization Forces paramilitary burn the US flag during a demonstration outside the US embassy in Baghdad. Photo: AFP/Ahmad al-Rubaye

Thousands of Iraqi supporters of the largely Iranian-trained Hashed al-Shaabi paramilitary force marched on the US embassy on Tuesday, furious over the deaths of 25 pro-Iranian militia members in US air strikes.

Read more: Iraqi militiamen hurl stones at US Embassy, prepare for extended stay

They set a security post on fire, breached one of the compound's outer walls, and threw rocks but were repelled by US troops, who used tear gas to defend the building.

On Wednesday, hundreds of demonstrators remained outside the embassy, despite orders from the Hashed al-Shaabi militia for an end to the sit-in.

US President Donald Trump tweeted that Iran would pay a "very BIG PRICE" for any lives lost or damage caused.