Iraqi security forces backed by Shiite and Sunni pro-government fighters bombard Islamic State positions outside Fallujah, 40 miles west of Baghdad. (AP)

— The Iraqi government said Monday that it had launched a broad military offensive against Islamic State strongholds in the country’s Anbar province, buttressed by a flurry of airstrikes conducted by the U.S. military.

Defense ministry officials said the operation began at dawn and involved a mix of army and police forces, Shiite militias and local Sunni tribal fighters.

Iraq’s government has struggled to regain territory in Sunni-majority Anbar since Islamic State fighters swept through the region last year. Government officials launched a similar offensive in May shortly after the provincial capital of Ramadi fell to the militants, but the operation quickly sputtered.

U.S. military aircraft and other allied forces helped clear the way for the offensive with an intensive bombing campaign Sunday in Ramadi, conducting 29 airstrikes there against 67 Islamic State targets. U.S. officials said the strikes were approved by the Iraqi defense ministry but otherwise had little to say about U.S. involvement in the broader campaign in Anbar.

Ground clashes took place Monday between Islamic State fighters and Iraqi forces on the outskirts of Ramadi and the province’s other main city, Fallujah.

Iraq’s Shiite militias have been on the offensive for days on the outskirts of Fallujah and claim to be leading operations there. But Hadi al-Amiri, the leader of the Badr Organization, one of Iraq’s most prominent Shiite militias, told Iraqi television that an attack on Fallujah would not be launched until after the Muslim Eid holiday, which falls this weekend, to give civilians time to leave the Sunni city. There are an estimated 50,000 civilians remaining in Fallujah.

While Iraq’s Iranian-backed Shiite militias have been pushing for an offensive on Fallujah, U.S. officials have advised they first target Ramadi before Islamic State militants have a chance to dig in. Now it appears the assaults may happen simultaneously.

Also Monday, the Iraqi government took delivery of its first four F-16 fighter jets, which it said would be deployed in Anbar within days. The long-awaited jets are among 36 ordered from the United States. They are the first new planes that Iraq has acquired since the U.S.-led invasion in 2003.

After Islamic State’s assault last summer, Iraq rushed to buy secondhand Sukhoi jets from Russia and China in an attempt to beef up its airpower while the F-16 deliveries were delayed.

Whitlock reported from Washington.