IRBIL, Iraq (AP) — Iraq's Kurdish fighters have lost more territory in Iraq, a day after Iraqi forces pushed them out of the disputed oil-rich city of Kirkuk.

In the town of Sinjar, commander of the local Yazidi militia, Masloum Shingali, says the Kurdish forces left before dawn on Tuesday, allowing Shiite-led militiamen who are fighting with Iraqi forces to move into the town.

Shingali says there was no fighting and that the Kurdish forces "left immediately, they didn't want to fight."

Town Mayor Mahma Khalil says the Popular Mobilization Forces, a predominantly Shiite militia coalition, is securing Sinjar.

On Monday, Iraqi troops pushed their Kurdish allies in the battle against the Islamic State group out of Kirkuk, seizing oil fields and other facilities amid soaring tensions over last month's Kurdish vote for independence.