BAGHDAD — The U.N. children’s fund on Wednesday issued a stark warning to Iraqi troops and Islamic State militants in the battle for Fallujah to spare the children, the most vulnerable among tens of thousands of civilians trapped in the city west of Baghdad.

Iraqi forces backed by U.S.-led airstrikes and mainly Shiite militias launched an operation more than a week ago to recapture Fallujah, which has been held by the extremist group for more than two years.

More than 50,000 people are believed to be trapped inside the Sunni majority city, about 65 kilometers (40 miles) west of Baghdad. Government forces have imposed a tight blockade on the city and IS militants are reportedly preventing residents from leaving.

UNICEF estimated the number of the children trapped with their families inside the city at about 20,000, warning that they face a dire humanitarian situation, in addition to the risk of forced recruitment by IS.

The organization called on all parties to “protect children inside Fallujah” and “provide safe passage to those wishing to leave the city.”

Iraqi special forces meanwhile continued their push into the city from its southern edge, said Brig. Haider al-Obeidi, who said “fierce” clashes were underway Wednesday.

Iraqi Prime Minister Haider al-Abadi praised the “remarkable advance” by the troops during a visit to the Fallujah Operation Command and vowed to “hoist the Iraqi flag inside Fallujah in the coming few days.”

Al-Abadi said IS was using civilians as human shields, and that the government has called on residents to leave through safe corridors or stay inside their homes.

Fallujah was the first large city in Iraq to fall to IS and it is the last major urban area controlled by the extremist group in western Iraq. The Sunni-led militants still control Iraq’s second-largest city, Mosul, as well as smaller towns and areas in the west and north.

The fight for Fallujah is expected to be protracted because IS 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.

The United Nations meanwhile said Wednesday that violence claimed the lives of at least 867 Iraqis in May, an increase from the previous month.

In its monthly report, the U.N. mission to Iraq said at least 468 civilians were among the dead, while the rest were members of the security forces. A total of 1,459 Iraqis were wounded last month, it said.

In April, at least 741 Iraqis were killed and 1,374 wounded. The figures do not include casualties from the western Anbar province, where Iraqi forces are battling IS militants in Fallujah and other areas.

Baghdad was the worst affected in May, with 267 civilians killed and 740 wounded, mainly in a series of bombings targeting security forces and the country’s Shiite majority.