Iraqi pro-government forces advance toward Fallujah on May 23, 2016, as part of a major assault to retake the city from Islamic State. / AFP PHOTO / AHMAD AL-RUBAYEAHMAD AL-RUBAYE/AFP/Getty Images (Ahmad Al-Rubaye/AFP/Getty Images)

Iraqi forces backed by U.S. warplanes advanced on Islamic State fighters in Fallujah on Monday, commanders and officials said, in the opening salvo of a fresh offensive to retake the militant-held city where nearly 100 Americans died in the early years of the Iraq War.

“Our forces are advancing, and things are going much better than we expected,” Iraqi Prime Minister Haider al-Abadi said Monday from the operations command center east of the city.

The Islamic State seized Fallujah, in Sunni-majority Anbar province, more than two years ago.

On Monday, the popular mobilization forces — an umbrella group for Iraq’s largely Shiite militias — announced that they had retaken the nearby city of Garma, where pro-government fighters had been bogged down battling the militants for months.

“The enemy is collapsing,” Abadi said. “Our message to civilians is that these operations are to save you from Daesh,” he said, using the Arabic acronym for the Islamic State.

The long-awaited offensive was announced late Sunday, and Iraqi police, counterterrorism forces, tribal fighters and Shiite militias were participating in the battle, authorities said.

Fallujah has long been a hotbed of resistance, and Islamic State fighters swept into the city in early 2014 on the back of an anti-government uprising in the area. Since then, the city has been ruled by the militants and has suffered from crippling shortages of food, medicine and fuel, residents and the United Nations have said.

Aid has not reached Fallujah since the government in December recaptured Ramadi, the provincial capital about 32 miles to the west, the U.N. refugee agency said in a statement Monday. Supply routes were cut off by Iraqi forces and other armed groups, the United Nations said, preventing civilians from leaving.

Iraq’s military said Monday that it had wrested control of the area of Niaimiyah, south of the city. It also said that an Iraqi F-16, supplied by the United States, struck an Islamic State bombmaking factory and hit rocket launchers in the city.

Since May 17, U.S.-led “coalition air power has struck 21 targets in and around Fallujah,” Col. Steve Warren, a Baghdad-based spokesman for the coalition, posted on Twitter on Monday.

Iraqi security forces, he said, were “meeting light to moderate resistance.”

Iraqi Prime Minister Haider al-Abadi meets with Iraqi military officers during his visit to a military base near Fallujah, May 23, 2016. EPA/IRAQI PRIME MINISTER OFFICE/HAND HANDOUT (Iraqi Prime Minister Office/Hand/EPA)

In recent months, pro-government forces have recaptured swaths of Anbar province from the group, including the city of Hit and the nearby town of Rutbah.

But while Iraqi forces appeared to have breached the militants’ defenses on the outskirts of Fallujah, the Islamic State is thought to have fortified its position in the center of the city.

Iraq’s military spokesman, Brig. Gen. Yahya Rasool, said Monday that the Islamic State has only 400 to 600 fighters in Fallujah. But the government also believes that as many as 70,000 civilians are still in the city. Fallujah’s cellphone network was down Monday, and residents could not be reached.

Iraqi forces have called on civilians to leave or stay home and away from Islamic State headquarters.

“This is a dangerous challenge, but the important thing is that we preserve the lives of civilians,” Abadi said Monday. “We demanded that they leave the city through secure roads,” he said. But “if they can’t, they should stay inside their homes.”

Another concern is that Shiite militias, which have been accused of crimes against Sunni civilians, would take revenge on Fallujah’s local population.

Abadi said that the plan to retake Fallujah was put into place more than two months ago but that security breaches in Baghdad had hindered the offensive. In recent weeks, car-bomb and other suicide attacks have killed more than 200 people in the capital.

“But now it has started,” he said. “God willing, the operation will end with the entire liberation of Fallujah.”

Cunningham reported from Istanbul.