Iraqi government-run camps struggled on Sunday to shelter people fleeing Fallujah, 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 Fallujah, 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 Fallujah 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.

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