More than 13,000 families have fled Fallujah in the past few days amid clashes and shelling after the city fell to Al-Qaeda-linked militants, the Iraqi Red Crescent said on Wednesday.

"Most of them are now living in schools, public buildings or with relatives," Red Crescent official Mohammed al-Khuzaie said in a statement.

Khuzaie said the organisation had provided humanitarian assistance to more than 8,000 families in the past three days across predominantly Sunni Arab Anbar province.

Fallujah and parts of the Anbar provincial capital Ramadi farther west have been outside government control for days -- the first time militants have exercised such open control in major cities since the height of the insurgency that followed the US-led invasion of 2003.

The violence in Anbar, which began on 20 December with the removal of a Sunni Arab anti-government protest camp, has killed more than 250 people -- the worst unrest to hit the province in years.