An Iraqi military commander says his forces are battling Islamic State militants in the northern neighborhoods of Fallujah days after most of the city was declared liberated.

Brig. Gen. Haider al-Obeidi told The Associated Press on Monday that militants are holed up in houses and buildings, saying he hopes to clear them out "in the coming few days."

Al-Obeidi says most of the fighters are foreigners who cannot melt into the local population or sneak into other parts of the country still controlled by the extremist group. They include snipers and fighters armed with rocket-propelled grenades.

The Fallujah offensive began in late May, and IS defenses in much of the city collapsed abruptly on Friday. It is located 40 miles (65 kilometers) west of Baghdad.