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At least 20,0000 children are trapped in Fallujah with limited food and water as coalition-backed Iraqi troops fight to retake the city from ISIS, the U.N.'s children's agency warned Wednesday.

UNICEF said food and medicine are running out and clean water is in short supply in the Islamist-controlled city, about 40 miles west of Baghdad.

Iraqi government troops — backed by air support from the U.S.-led coalition — launched a military operation over a week ago to recapture Fallujah, which has under ISIS control since 2014.

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At least 20k children trapped in Fallujah, #Iraq - food & medicine running out & clean water in short supply https://t.co/Vb6w6loN5z — UNICEF (@UNICEF) June 1, 2016

Very few families have been able to flee the city since the start of the offensive, UNICEF’s Iraq representative Peter Hawkins said in a statement.

“Most have moved to two camps while others have sought refuge with relatives and extended families,” he said. "At least 20,000 children remain trapped in the city.

He called on all sides to provide safe passage for those wishing to leave.

Related: ISIS May Be Using ‘Human Shields’ in Fallujah, U.N. Warns

“As the violence continues to escalate in Fallujah and across Iraq, we are concerned over the protection of children in the face of extreme and rising danger,” Hawkins said. “Children face the risk of forced recruitment into the fighting, strict procedures for security screening and separation from their families.”

The U.N. has already raised concerns that ISIS has been using families as human shields.

Brig. Yehya Rasool, the spokesman for Iraq's Joint Operation Command, told NBC News Wednesday that troops had liberated the district of Nuaimiya, about two miles south of the city now will continue their advance towards areas closer to the center of Fallujah.

"In the north, Iraqi forces were able to storm into Saqlawiyah, 5.5 miles from the center of Fallujah, after heavy clashes," he said. "The fighting to retake over the district is still going on."

The fight for Fallujah is expected to be protracted because ISIS has had more than two years to dig in. Hidden bombs are believed to be strewn throughout the city, and the presence of trapped civilians will limit the use of supporting airstrikes.

Fallujah is the last major urban area controlled by ISIS in western Iraq. It still holds the country's second-largest city, Mosul, in the north, as well as smaller towns and patches of territory in the country's west and north.