An Iraqi commander says special forces have retaken the main government compound in Fallujah from Islamic State militants.

The breakthrough came after nearly four weeks of intense fighting in the city, which is the bastion of the militant group.

"The liberation of the government compound, which is the main landmark in the city, symbolises the restoration of the state's authority in Fallujah," said Iraq's federal police chief Raed Shaker Jawdat.

Troops were supported from the air by the US-led coalition and the Iraqi air force.

Lieutenant General Abdulwahab al-Saadi, overall commander of the operation, said there had been little resistance from IS.

"The counter-terrorism service and the rapid response forces have retaken the government compound in the centre of Fallujah," he said.

"There is a mass flight of Daesh [IS] to the west that explains this lack of resistance. There are only pockets of them left, and we are hunting them down."

More to follow.