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ISIS is reportedly using civilian "human shields" in Fallujah as U.S.-backed Iraqi forces push into the militant-held city, the U.N. warned Tuesday.

The alarm was sounded as Iraq's military announced it was less that 2 miles from the center of Fallujah, which has been under ISIS control since 2014.

The U.N. refugee agency said an estimated 3,700 people have fled Fallujah over the past week and that there were reports of civilian casualties from heavy shelling as the battle has heated up.

“There are also reports of several hundred families being used as human shields,” the agency's spokesperson William Spindler told a press conference.

"A human catastrophe is unfolding in Fallujah"

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A spokesman for Iraq's counter-terrorism unit, which is leading the charge, told NBC News that the pro-Baghdad forces were fighting in the Nuaimiya district in southern Fallujah.

"U.S.-led coalition and the Iraqi Air Force are providing aerial coverage for our ground forces," the spokesman, Sabah Nuaman, added.

Monday's drive into Nuaimiya — a mainly agricultural area south of the city — was Iraqi forces’ first attempt to enter Fallujah after concentrating on flushing militants out of the surrounding areas.

Brig. Yahya Rasool, a spokesman for U.S. Joint Operations Command which is coordinating the fight against ISIS, said Iraq forces were preparing to storm into the city within 24 hours.

Iraqi security forces gather near Fallujah on Tuesday. THAIER AL-SUDANI / Reuters

Meanwhile, two special forces officers told The Associated Press that pro-government Iraqi fighters battling to get into Fallujah had fended off a four-hour ISIS attack earlier on Tuesday.

The AP reported that ISIS militants had used tunnels, deployed snipers and sent six explosives-laden cars to hit the troops but they were destroyed before reaching their targets.

Related: U.S. Strike Kills ISIS' Fallujah Commander, Military Says

While military officials claimed continued victories, a top humanitarian official warned of an impending humanitarian disaster for the 50,000 civilians left in the city

"A human catastrophe is unfolding in Fallujah," Jan Egeland, Secretary General of the Norwegian Refugee Council, said in a statement. "Warring parties must guarantee civilians safe exit now, before it's too late and more lives are lost.”

The organization's country director for Iraq, Nasr Muflahi, said the stories coming out of Fallujah were "horrifying."

"A lack of food, medicine, safe drinking water and electricity are pushing families to the brink of desperation," Muflahi added.

Fallujah is 40 miles west of Baghdad. ISIS still controls parts of the country's north and east and Iraq’s second largest city, Mosul.