BAGHDAD (Reuters) - Iraqi government-run camps struggled on Sunday to shelter people fleeing Falluja, as the military battled Islamic State militants in the city’s northern districts.

Prime Minister Haider al-Abadi declared victory over the jihadists on Friday after troops reached the city center, following a four-week U.S.-backed assault.

But shooting, suicide bombs and mortar attacks continue.

More than 82,000 civilians have evacuated Falluja, an hour’s drive west of Baghdad, since the campaign began and up to 25,000 more are likely on the move, the United Nations said.

Yet camps are already overflowing with escapees who trekked several kilometers (miles) past Islamic State snipers and minefields in sweltering heat to find there was not even shade.

“People have run and walked for days. They left Falluja with nothing,” said Lise Grande, U.N. Humanitarian Coordinator for Iraq. “They have nothing and they need everything.”

The exodus, which is likely to be many times larger if an assault on the northern Islamic State stronghold of Mosul goes ahead as planned later this year, has taken the government and humanitarian groups off guard.

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With attention focused for months on Mosul, Prime Minister Haider al-Abadi said in May that the army would prioritize Falluja, the first Iraqi city seized by the militants in early 2014.

He ordered measures on Saturday to help escapees and 10 new camps will soon go up, but the government does not even have a handle on the number of displaced people, many of whom are stranded out in the open or packed several families to a tent.

One site hosting around 1,800 people has only one latrine, according to the Norwegian Refugee Council.

“We implore the Iraqi government to take charge of this humanitarian disaster unfolding on our watch,” the aid group’s country director Nasr Muflahi said.

“WE JUST WANT OUR MEN”

Iraq’s cash-strapped government has struggled to meet basic needs for more than 3.4 million people across Iraq displaced by conflict, appealing for international funding and relying on local religious networks for support.

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Yet unlike other battles, where many civilians sought refuge in nearby cities or the capital, people fleeing Falluja have been barred from entering Baghdad, just 60 km (40 miles) away, and aid officials note a lack of community mobilization.

Many Iraqis consider Falluja an irredeemable bulwark of Sunni Muslim militancy and regard anyone still there when the assault began as an Islamic State supporter. A bastion of the Sunni insurgency against U.S. forces following the 2003 invasion, it was seen as a launchpad for bombings in Baghdad.

The participation of Shi’ite militias in the battle alongside the army raised fears of sectarian killings, and the authorities have made arrests related to allegations that militiamen executed dozens of fleeing Sunni men.

Formal government forces are screening men to prevent Islamic State militants from disguising themselves as civilians to slip out of Falluja. Thousands have been freed and scores referred to the courts, but many others remain unaccounted for, security sources told Reuters.

At a camp in Amiriyat Falluja on Thursday, Fatima Khalifa said she had not heard from her husband and their 19-year-old son since they were taken from a nearby town two weeks earlier.

“We don’t know where they are or where they were taken,” she said. “We don’t want rice or cooking oil, we just want our men.”