Iraqi forces are shelling Islamic State targets in Falluja on the second day of an assault to retake the militant stronghold just west of Baghdad. (Reuters)

Iraqi forces pounded the city of Fallujah with artillery fire on Tuesday, as they sought to advance Prime Minister Haider al-Abadi’s offensive to reclaim a strategic area of Anbar province from the Islamic State militant group.

Hundreds of fighters aligned with the government, including federal police, SWAT forces and at least seven well-armed Shiite militia groups, flooded into the dusty scrubland around an abandoned cement factory reclaimed only the day before.

Nearby forces lobbed regular artillery fire at Fallujah, about three miles to the west. Capture of the largely Sunni Muslim city, whose seizure by the Islamic State in early 2014 foreshadowed the group’s later military success across Iraq, would be an important victory for the embattled Abadi.

On the factory grounds in an area called Harariyat, vehicles displaying the fighting factions’ emblems and flags rushed men and supplies in different directions as various commanders came and went. On a rise overlooking Fallujah, Shiite militiamen from the Badr Organization and Kitaeb Hezbollah, which the United States considers a terrorist group, celebrated their recent gains against the Sunni Islamist group, shouting pro-Shiite slogans and unleashing volleys of gunfire into the air.

The chaotic scene was a sign of what Iraqi commanders described as a battle being fought by “one hand,” meaning government, militia and tribal forces advancing together toward a common goal. It was also a sign of the challenge that the Iraqi government and its Western backers will face in coordinating what they hope is a final series of offensives by forces with varying loyalties, weaponry and skills.

Speaking during a visit to the factory, Lt. Gen. Raeed Shakir Jawdat, commander of the federal police, said the government and allied forces have dismantled dozens of car bombs and killed scores of Islamic State fighters. Some escaped by river, he said.

“Now the enemy is collapsing, and we are hunting them,” Jawdat said.

He spoke the day after the government said it recaptured the district of Garma, about 10 miles northeast of Fallujah. It was the initial move in an operation that officials in Baghdad hope will result in a rapid liberation of the city, allowing the government to turn its sights to a bigger prize, the major northern city of Mosul, which the Islamic State captured in June 2014.

Also Tuesday, Iraqi army units positioned in other areas near Fallujah took control of the villages of Luhaib and Albu Khanfar, the government said.

Iraqi commanders said Islamic State militants have put up a fierce fight around Fallujah in recent days, but they declined to share figures on the government’s casualties.

Iraqi pro-government fighters hold position in Shahabi village, east of Fallujah, on May 24 as part of a major assault to retake the city from the Islamic State. (Ahmad Al-Rubaye/AFP/Getty Images)

The Islamic State fired the occasional artillery round in response to the incoming fire. One landed in an overgrown field far behind the front lines, sending smoke into the air.

Maj. Gen. Saad Ali al-Harbiya, commander of operations west of Baghdad, said forces from the 1st, 6th, 4th and 17th Iraqi army divisions were taking part in the Fallujah operation, along with the police and militia units. So far, Sunni tribal fighters whom the United States has encouraged the Shiite-led government to arm have played a minimal role, officials said. The U.S. military said Sunni tribesmen would be advancing on the Islamic State from the west of the city.

U.S. and Iraqi aircraft carried out strikes in the Fallujah area Monday and Tuesday, officials said.

Harbiya spoke from a nearby field headquarters that Abadi visited Monday, an opportunity for the prime minister to burnish his commander-in-chief credentials as he battles a political crisis in Baghdad.

The outcome of the Fallujah operation will be crucial for Abadi, whose government was forced to declare a curfew last week after protesters stormed the heavily guarded Green Zone, where Abadi’s office and the U.S. Embassy are located.

As the second anniversary of Mosul’s collapse draws near, Abadi is under pressure to show he can deliver not just security, but also prosperity and political reform.

Iraqi commanders have promised that the operation in Fallujah will demonstrate that a mixed military force, including an important militia component, can function without the problems that have plagued previous offensives in places such as Tikrit and Jurf al-Sakhr, where Sunni residents accused Shiite militiamen of arbitrary arrests, looting and abuse.

Although Shiite militias have said that they will not press into the city proper, their presence in Anbar and other areas is a complication for the United States and its allies, which have sought to limit their support to government and Sunni tribal forces. But Abadi’s government, in need of combat power, continues to rely heavily on the Shiite militias.

Many militiamen are suspicious of the residents of Fallujah, where the Islamic State found fertile ground when it first appeared in force in late 2013.

Hamid Abeed Mutlak, a member of parliament from Fallujah, urged the government to prevent militiamen from entering the city. He said residents were terrified of sectarian retaliation, even as they struggled with a prolonged lack of necessities such as food and medicine.

Mutlak said the operation, which is only in its opening days, was already taking a toll on civilians. He said 11 members of a single family were killed Monday by shelling from government-aligned forces.

Brig. Gen. Yahya Rasool, an Iraqi military spokesman, denied that civilians were killed. He said that the shelling targeted Islamic State headquarters and that civilians were warned to stay away.

“The purpose of this operation is to save them from the injustice of the terrorism of Daesh,” he said, using an Arabic acronym for the Islamic State.

Military and police officials said they were awaiting orders from Baghdad to begin a ground advance into Fallujah. “We are getting very close to this area,” Harbiya said.

He said U.S. forces were providing assistance from Baghdad, helping the military identify positions occupied by militants. Italian advisers also are lending remote support to the federal police, officials said.