BAGHDAD — Kurdish forces said they drove ISIS militants out of villages near the oil city of Kirkuk in northern Iraq on Wednesday, in an offensive backed by airstrikes from the U.S.-led coalition.

The assault consolidated their control over Kirkuk and brought the peshmerga, the military forces of Iraq’s autonomous Kurdistan region, closer to the insurgents’ bastion of Hawijah, around 34 miles west of Kirkuk.

Around 3,500 peshmerga took part in the operation beginning early on Wednesday southwest of Kirkuk, the Kurdistan region’s security council said in a statement.

Kurdish forces had secured 55 square miles including a number of villages and the Ghara heights, “further diminishing ISIS’s ability to attack peshmerga forces and putting additional pressure on ISIS in Hawijah.”

Kurdistan’s security council said at least 40 ISIS militants had been killed in combat and others were seen fleeing the battlefield toward Hawijah and surrounding areas. Fifteen peshmerga also died, according to a source in a Kirkuk hospital.