(CNN) Nearly 1,000 suspected ISIS militants have surrendered to Kurdish forces near Kirkuk in the last few weeks, Kurdish Gen. Shawrash Hakim said Tuesday.
Most of the suspects fled among civilians who left Hawija, about 40 miles (64 kilometers) west of Kirkuk, after Iraqi troops launched a military operation to retake the town of about 100,000 people from ISIS' grasp last month.
The offensive began September 21. Last week, Iraqi troops announced they had retaken the city center, one of the terror outfit's last remaining strongholds, though operations remained ongoing
"Most ISIS militants have surrendered to our forces, but some of them were detained after they tried to sneak in among their families," Hakim said. "We know them. We have a long list of names. They can't hide from us."
The suspects' families were sent to camps for the internally displaced in Dibis and the surrounding area, Hakim said.
Lt. Col. Ali Mohammed, a Kurdish security officer in Dibis, estimated that about 7,000 people had fled Hawija since the military campaign began.
However, the UN's Office for the Coordination of Humanitarian Affairs reported a higher total last week, with spokesman Jens Laerke saying at least 12,500 people had fled the fighting.
Laerke also reported -- two days before Iraqi troops said they had control of the city center -- that another 78,000 were possibly trapped by ISIS.
The Norwegian Refugee Council, which has been working with families fleeing Hawija since October 2015, says many of the internally displaced have been left with no homes to which they can return.
"No one must be forced to return to the newly retaken areas," said Heidi Diedrich, the group's country director in Iraq. "It is crucial for Iraq's future that all returns are informed, voluntary and happen only after areas are safe and basic services can be provided."
ISIS has been losing ground in Iraq since US-backed Iraqi forces captured the group's stronghold of Mosul in July after a nine-month battle.
In August, ISIS was driven out of Tal Afar, a northwestern town captured by the terror group in June 2014.