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.

Iraqi forces pushed into the center of Fallujah on Friday, retaking a government complex and the central hospital. That evening Brig. Gen. Haider al-Obedi, with Iraq’s special forces, told The Associated Press his troops controlled 80% of the city.

Iraqi Prime Minister Haider al-Abadi said Friday that Fallujah had “returned to the embrace of the nation,” and that remaining Islamic State pockets would be “cleaned out within hours.”

But in recent days there have been persistent clashes between Iraqi forces and Islamic State fighters holed up in dense residential neighborhoods along the city’s northern edge.

Iraqi commander: Fallujah 'fully liberated' from ISIS

Read Next: Iraqi commander: Fallujah 'fully liberated' from ISIS

“What it looks like is (an IS) defensive belt around the city with not as stiff defenses inside,” Garver said, explaining that as Iraqi forces move out from the city center they may encounter additional pockets of stiff resistance.

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