Marine transfer a case containing the remains of Marine Corp Staff Sgt. Louis Cardin at Dover Air Force Base, Del., on Monday after he was killed in Iraq. (Cliff Owen/AP)

Iraqi forces backed by American airstrikes opened an operation Thursday seeking to drive the Islamic State out of a string of northern villages where U.S. troops twice came under attack over the past week and a U.S. Marine was killed.

Iraqi officials said it was the prelude to an offensive aimed at recapturing Mosul, the biggest city under Islamic State control and a longstanding priority for the Pentagon.

But Kurdish and U.S. military officials described a far more limited operation to clear the Islamic State from villages near Makhmour, about 40 miles southeast of Mosul and around 30 miles south of the Kurdistan regional capital of Irbil.

Makhmour is a front-line base for U.S., Iraqi Army and Kurdish fighters known as peshmerga.

This is an operation “to liberate villages in the vicinity of Makhmour,”said U.S. military spokesman Col. Steve Warren in Baghdad.

“They’ve had great success so far,” he added.

Backed by U.S. airstrikes, Iraqi army troops and local tribal fighters overran four villages, an Iraqi military statement said. Local news reports indicated that fighting was ongoing.

A U.S. Marine, Staff Sgt. Louis F. Cardin, of Temecula, Calif., was killed Saturday in rocket fire against Makhmour, and the small U.S. base there was attacked again on Monday by a small group of Islamic State fighters with guns and grenades.

The operation seeks to improve the safety of the troops at the base “because there will be less enemy nearby,” Warren said. The area, however, remains within rocket range, he added.

The Iraqi Army said four villages had been reclaimed in the operation: Nasr, Karmanda, Kuthela and Khurburdan.

Makhmour is expected to be an important staging point for an eventual operation to recapture Mosul, but U.S. and Kurdish officials say any such offensive is unlikely to occur for months or more.

Salim reported from Baghdad.