MOSUL, Iraq (Reuters) - Fly-blown corpses of Islamic State militants (IS) littered the streets of a district in Mosul on Tuesday as U.S.-backed Iraqi forces chipped away at the last remaining handful of districts under the jihadists’ control.

Seven months into the campaign to recapture Iraq’s second largest city, government forces say it is now in its final phase after opening a new front in the northwest of Mosul last week and gaining ground in several districts there.

Trapped in a shrinking area with no way out, the ultra hardline Sunni militants are hitting back with a barrage of suicide car bombs and snipers hidden among hundreds of thousands of civilians they are effectively holding hostage.

A Reuters reporter in the Harmat district, which has been partially retaken by the Interior Ministry’s elite Emergency Response Division, said there was heavy fighting there on Tuesday.

Jets flying overhead conducted air strikes and helicopters strafed IS positions while several car bombs exploded in the distance. Heavy sniper and mortar fire could be heard.

A spokesman for the Emergency Response Division said 250 Islamic State members had been killed in Harmat over the past 5 days.

Hundreds of families streamed out of Harmat, 17 Tammuz and other front-line districts, joining an exodus of 435,000 people who have been displaced from the western half of Mosul since Iraqi forces began attacking it in February, according to U.N. figures.

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Traveling in the back of a van carrying civilians to safety, 44-year-old Abu Ahmed said the militants had forced 48 people into the basement of his home in the Musherfa district before opening fire from it. The aim was to goad Iraqi forces into striking the house and thereby turn civilians against them.

“They tried to scare us into helping them, they said the army would rape our women. But we didn’t believe them.”

CAMOUFLAGE

With no escape route, a growing number of militants are trying to leave the city by camouflaging themselves among fleeing civilians, Brigadier General Mahdi Abbas Abdallah of the Rapid Response Division said on Tuesday.

“We are conducting checks on all the fleeing families.”

Conditions in the handful of districts still under militant control are increasingly desperate as food runs out and civilians are killed under bombardment.

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A resident of the 17 Tammuz district said at least 10 people including his neighbor’s son had died as a result of air strikes and mortar fire since Monday: “The rockets are falling like rain over our heads,” he told Reuters by phone.

Militants were burning civilian vehicles to produce a smokescreen against aerial surveillance and had taken up position on the roofs of tall buildings wearing suicide belts, he said. “The fear and confusion is visible on their faces.”

The elite Counter Terrorism Service (CTS) retook an industrial area on Tuesday, Lieutenant General Abdul Ameer Rasheed Yarallah, who commands the campaign, said in a statement.

A woman in the adjacent Islah al-Ziraai neighborhood, which remains under Islamic State control, said she could now see the Iraqi flag in the distance.

“We will die of hunger if they don’t reach us within a week,” said the woman, who has resorted to eating weeds. “Despite the violent bombardment, we are happy that the Iraqi forces are approaching us.”

Islamic State seized Mosul in a shock offensive across northern and western Iraq in 2014 but have lost much of their gains to resurgent government forces over the past year. Still, even defeat in Mosul would still leave IS in control of swathes of Syria and Iraqi territory near the Syrian border.