Only a third of Fallujah has been “cleared” of the Islamic State, the U.S.-led coalition said Tuesday.

The announcement comes days after the Iraqi government declared victory in the besieged city.

Other parts of the city are “contested,” said U.S. Army Col. Christopher Garver, the Baghdad-based spokesman for the coalition, with clashes underway between Iraqi security forces and Islamic State fighters.

Most of the cleared area is in the south of the city. “Clearing operations continue outward from the city center,” Garver added.