Fallujah city centre completely under control of forces linked to al-Qaeda
Hadi Razeij, head of the Anbar police force, said police had left the city centre entirely and had positioned themselves on the edge of town.
He said on Arabic language broadcaster al-Arabiya: "The walls of the city are in the hands of the police force, but the people of Fallujah are the prisoners of ISIL."
Fallujah, along with nearby provincial capital Ramadi, were strongholds of Sunni insurgents during the US-led war. Al-Qaeda militants largely took them over earlier this week.
The escalating tension shows that the civil war in Syria, where mostly Sunni rebels are battling President Bashar al-Assad, who is backed by Shia power Iran, is spilling over to other countries like Iraq, threatening its delicate sectarian balance.