The operation follows months of planning and preparation in coordination with a U.S.-led military coalition that is backing Iraqi forces with airstrikes.
Iraqi forces have long had the city surrounded, but a major buildup of forces became evident in recent days as Shiite militias working alongside the Iraqi army moved military equipment to the area and officials suggested an operation was imminent.
Before the start of operations Sunday, the Iraqi government appealed to residents of Fallujah to prepare to leave, even urging them to raise white flags at their houses if they couldn’t.
The military’s Joint Operations Command said that civilian families would be allowed to leave the city through designated safe passages, though it didn’t specify how departures from the city would be arranged.
The Iraqi army, counterterrorism forces, police, tribal fighters and Shiite militias were taking part in the operation, according to the military.
Eissa al-Issawi, the exiled mayor of Fallujah, said Islamic State militants were retreating from the outskirts to the center of the city Sunday as the operation drew nearer
Civilians inside were eager for any relief from isolation, 74-year-old resident Mohessen Hossam said. Many people have died of starvation in the city since Iraqi forces imposed a blockade last year, residents have said, although the precise toll is impossible to measure.
If successful, the recapture of Fallujah would leave Mosul as Islamic State’s only major foothold in Iraq. Iraqi forces have long been gearing up for Mosul’s recapture, which is expected to be complex in part because of its size: Mosul has a population of around 1 million, about three times the size of Fallujah’s before Islamic State took the city.
Despite its smaller size, the Fallujah battle isn’t expected to be easy. The city is inhabited mostly by Sunni Muslims, many of whom resent any incursion by Iran-backed Shiite militias that form a significant part of the force fighting for control. To avoid triggering sectarian bloodshed, Shiite militias aren’t expected to be part of the forces that retake the city center.
Nonetheless, Ibrahim al-Jumaili, a Fallujah native who left three months ago and is now living just outside the city, said he had spoken to people inside Sunday who were concerned about being targeted by Shiite militias.
Fallujah has also been a difficult objective for invading armies before, including for the U.S., which took it in 2004 and held it for two years before handing control to the Iraqi government. The city became a focal point for Sunni discord after a Shiite-led government took power in Baghdad after the U.S.-led invasion.
Islamic State took control of Fallujah in December 2013, making it one of the group’s first big territorial gains, preceding its establishment of a base in Raqqa in Syria. Mosul only fell under its control in summer 2014.
As Iraqi forces turned the tide since last year, Islamic State has switched tactics, focusing more on terrorist attacks in populated areas than it had previously. A wave of Islamic State attacks in and near Baghdad earlier this month—most of them suicide bombings—killed almost 200 people.