Shiia fighters and Iraqi security forces advance toward Fallujah, Iraq, on May 25, 2016.Thaier Al-Sudani / Reuters

Several days after Iraqi military forces launched an offensive against Islamic State militants in Fallujah, thousands of civilians in the city are at “extreme risk,” the United Nations said Thursday.

“We are receiving distressing reports of civilians trapped inside Fallujah who are desperate to escape to safety, but can’t,” said Lise Grande, the UN humanitarian coordinator for Iraq, in a statement. “Parties to the conflict are obliged to uphold international humanitarian law and do everything possible to protect civilians and ensure they receive lifesaving assistance.”

The Iraqi city, located east of Baghdad, has been under ISIS control since January 2014. Iraqi troops, police, and Shia militias approached the city late Sunday into early Monday, under the cover of airstrikes from the U.S.-led coalition that has been fighting the terrorist group for nearly two years.

At least 50,000 people are believed to be in the city, according to the UN. About 800 have fled and reached safety since the operation began, and “some families report having to walk for hours under harrowing conditions to reach safety,” the UN said. Some have died as they tried to escape, according to observers on the ground.

“Food supplies are limited and tightly controlled,” Grande said, citing people who have left the city. “Medicines are exhausted and many families have no choice but to rely on dirty and unsafe water sources.”

Iraqi authorities have opened a camp in Ameriyat al-Fallujah, located about 30 kilometers, or 19 miles, from Fallujah. Becky Bakr Abdulla, a media coordinator at the Norwegian Refugee Council, arrived at the shelter Tuesday and spoke with families who fled Fallujah only days before. She described on Thursday their harrowing experiences to The Guardian’s Holly Young Thursday:

The families I met were in a state of shock and spoke about the ordeal of their escape. They were among the 21 families in Al Iraq camp, out of approximately 114 who we believe have escaped the city so far. One woman, whose family was told by armed opposition groups that they would be shot if they tried to flee, waited until night-time to make a move. They removed their shoes and sandals so they were not heard as they started running.

Nine-year-old Mohammed told me how, once outside his house, he ran for hours until his feet were in pain. He escaped alongside 16 or 17 other families, with one person in front checking that the coast was clear of fighters and planted explosives. Once these families reached the checkpoint leading out of the town they waved white flags made of cloth to prevent them from being shot. After that they kept moving, 30km on to the Al Iraq camp.

Many others have not been so lucky. I’ve just heard the news of one father trying to escape while carrying his two sons in his arms. He stepped on an IED planted on the outskirts of the city. All three were killed immediately.

The residents of Fallujah have been effectively trapped for more than two years, prohibited by ISIS from leaving. According to the Human Rights Watch, humanitarian workers have been unable to reach the city since Iraqi troops and U.S. coalition forces in December regained control of the nearby city of Ramadi after six months of ISIS control. Iraqi forces in February blocked supply routes between the two cities in an attempt to hinder ISIS operations.

“Iraqi activists who are in touch with Fallujah families said that people were reduced to eating flat bread made with flour from ground date seeds and soups made from grass,” Human Rights Watch said in a statement in April. “What little food remains is being sold at exorbitant prices.”

Fallujah was the first of several cities in Iraq ISIS captured in 2014 as it grew in strength and territory. U.S. and Iraqi officials hope next to attempt to retake Mosul, a city north of Fallujah that was overrun by militants in June 2014.

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