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. […]