TIKRIT, Iraq (Reuters) - 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 100 km (60 miles) south of Mosul, has been surrounded for months by Iraqi troops and Iranian-backed Shi’ite Muslim militias allied to the government. But the army, backed by local police and Sunni Muslim 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 Islamic State 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.

A spokesman for the United Nations refugee agency UNHCR said there had been no displacement on Tuesday and only 32 people dislodged from their homes on Wednesday to a nearby reception center.

Iraqi authorities hope the course of battle will allow most residents to shelter in place to avoid creating a humanitarian crisis as forces move towards Mosul, where more than a million people are still living.

The U.S. envoy to the anti-Islamic State coalition said on Wednesday the coalition was already taking steps to ensure there would be no repeat in the Mosul offensive of the abuses seen in the wake of the recapture of Falluja in June, when Shi’ite militias detained, abused and tortured scores of Sunni civilians.

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The disposition of forces and the treatment of Shirqat’s residents will be closely watched by the Sunni residents of Mosul, who have a historic mistrust of the forces of successive Shi’ite-led governments in Baghdad.

U.S. and Iraqi officials have said the push on Mosul could begin in October, though there are concerns that not enough planning has been done for how to manage the city, Iraq’s second-largest, if and when Islamic State is expelled.

Hawija, east of Shirqat, is the other remaining Islamic State bastion south of Mosul. The group also controls the city of Tel Afar, west of Mosul towards the Syrian border.