BAGHDAD — The city center of Iraq’s Fallujah has fallen completely into the hands of fighters from the al-Qaida-linked Islamic State in Iraq and Levant, police said Saturday.

Hadi Razeij, head of the Anbar province police force, said police had left the city center entirely and had positioned themselves on the edge of town.

“The walls of the city are in the hands of the police force, but the people of Fallujah are the prisoners of ISIL,” he said, speaking on Arabic language satellite broadcaster al-Arabiya.

Fallujah, along with nearby provincial capital Ramadi, was a stronghold of Sunni insurgents during the U.S.-led war. Al-Qaida militants largely took both cities over last week and have been fending off incursions by government forces there since.

The U.S. State Department expressed its concern in a statement, saying it would continue to work with Iraqi authorities and tribes allied against ISIL “to defeat our common enemy.”

“We are also in contact with tribal leaders from Anbar province who are showing great courage as they fight to eject these terrorist groups from their cities,” Deputy Spokesperson Marie Harf said.

Government troops, backed by Sunni tribesmen who oppose al-Qaida, have encircled Fallujah for several days, and have entered parts of Ramadi. On Friday, troops bombarded militant positions outside Fallujah with artillery, a military official said, speaking on condition of anonymity as he was not authorized to release information.

Anbar province, a vast desert area on the borders with Syria and Jordan with an almost entirely Sunni population was the heartland of the Sunni insurgency that rose up against American troops and the Iraqi government after the 2003 U.S.-led invasion that toppled Saddam Hussein. The insurgency was fueled by anger over the dislodgment of their community from power during Saddam’s rule and the rise of Shiites. It was then that al-Qaida established its branch in the country.

Fallujah became notorious among Americans when insurgents in 2004 killed four American security contractors and hung their burned bodies from a bridge. Fallujah, Ramadi and other cities remained battlegrounds for the following years, as sectarian bloodshed mounted, with Shiite militias killing Sunnis.

In a speech in Baghdad, Prime Minister Nouri al-Maliki said government forces would press on to clear the province of militants.

“There will be no retreat until we eliminate this gang and rid the people of Anbar of their evil acts,” he said. “The people of Anbar asked the government for help, they called us to come to rescue them from terrorists.”