Lt Gen Rasheed Fleih, who leads the Anbar Military Command, told state television that "two to three days" are needed to push the militants out of Fallujah and parts of Ramadi.

Lt Gen Fleih said pro-government Sunni tribes are leading the operations while the army is offering aerial cover and logistics on the ground, the newspaper said.

Fighting has raged in Iraq's western Anbar province since Monday, with troops from the Islamic State in Iraq and the Levant taking over the centre of Fallujah and some parts of Ramadi.

Residents say it has been quiet in Fallujah since Saturday night, while sporadic clashes took place in Ramadi.