Gen. Yahya Rasool, announced in a televised statement that the operations started at dawn Monday.
Islamic State’s capture of Ramadi two months ago marked the biggest defeat for the Baghdad government since the militants swept through the north of the country last June and declared a caliphate in parts of Syria and Iraq straddling the border.
A second bomb in the Iskan district of western Baghdad killed two people on Sunday evening, medical sources said.
A string of bomb explosions, including two suicide attacks, have killed at least 21 people and wounded 62 in Shi’ite-dominated neighborhoods of Baghdad.
Hashed al-Shaabi said its forces were advancing northeast of Fallujah, an IS bastion which has escaped government control since early 2014 and where U.S. troops faced the toughest battles of their eight-year occupation.
At least 35 people have been killed in a spate of bomb attacks in the Iraqi capital, Baghdad, officials say.
Iraq was possibly going through the worst and most unsafe challenge to its territorial integrity, economic sustainability and human development capacity.
The Iraqi Air Force is also expected to participate in the operation to recapture the major city of Anbar province.
The Britain-based Syrian Observatory for Human Rights said Monday’s airstrikes killed 13, including six women, and wounded as many as 40. Having initially said it would prioritize Ramadi, it now appears to have turned instead to Falluja, which is located further downriver and closer to Baghdad – around 50 km (30 miles) west of the capital. On May 31, Syrian army airstrikes that hit a packed market in al-Bab killed around 70 people, majority civilians.