BAGHDAD — Iraqi forces backed by air strikes from the U.S.-led coalition gained complete control of the northern district of Shirqat on Thursday, bringing the military a step closer to a main push on Mosul later this year.

Brigadier-General Yahya Rasool, spokesman for the military’s joint operations command, said in a statement broadcast on state television that the district had been liberated from “the desecration of terrorism.”

Shirqat, on the Tigris river south of Mosul, has been surrounded for months by Iraqi troops and Iranian-backed Muslim militias allied to the government. But the army, backed by local police and Sunni tribal fighters, conducted the fighting this week and the militias did not appear to take part.

Iraqi forces advanced swiftly through the area after Prime Minister Haider al-Abadi announced the operation on Tuesday morning.

The area’s proximity to Iraqi supply lines reaching Qayyara air base further north, which will be used as a logistics hub for the push on Mosul, lends it strategic importance. A rocket attack on Tuesday that came within hundreds of meters of U.S. forces at the base is being tested for chemical agents.

Tens of thousands of civilians were thought to be trapped in the town and nearby villages, which have been under ISIS control since the group seized a third of Iraqi territory in 2014. But the operation has not generated the large-scale outflux seen in other recent campaigns.