HAMMAM AL-ALIL CAMP, Iraq (Reuters) - Thousands more people are fleeing Mosul every day since Iraqi troops began their push into the last Islamic State-held areas of the city last week, with food and water running out and the fighting killing increasing numbers of civilians.

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More than 22,000 people have fled Mosul since the U.S.-backed forces opened a new front in the northwest of the city on May 4 to try to finally dislodge the militants, the United Nations said on Wednesday, citing Iraqi government figures.

In the past two days alone, more than 11,000 people have passed through a screening site at the Hammam al-Alil camp south of Mosul.

Islamic State fighters are shooting people who try to escape, although some men have been allowed to go in exchange for taking militants’ families with them, said 40-year-old Umm Abdul Rahman, who fled the Musherfa district on Tuesday night.

One man waiting to be checked by security at Hammam al Alil had streaks of blood on his clothes from carrying a woman hit by an Islamic State sniper.

They join an exodus from Mosul of more than 600,000 people in the seven months since Iraqi forces began their offensive there. Roughly 400,000 of those are from the western side of the city which is bisected by the River Tigris.

The militants are now besieged in the northwestern corner, which includes the historic Old City center, the medieval Grand al-Nuri Mosque, and its landmark leaning minaret where their black flag has been flying since June 2014.

About ten families, some forced out of other areas of Mosul as Iraqi forces advanced, were now crammed into every house in the northwest, Abdul Rahman said.

“There is no water, no food. The bombardment is continuous,” she said, and the militants were setting civilian cars and trucks on fire to create smokescreens.

People are surviving on ground wheat boiled in water, 31-year-old Qatra al-Nada Abdullah said, because Islamic State fighters were keeping any food or water that is left for themselves.

“Even wheat is scarce,” she said.

Islamic State fighters are forcing people from their homes to use them as fighting positions, 62-year-old Umm Mohammed said as she clutched a packet of cigarettes forbidden under the militants’ rule.

She and her family had burned everything, even their own shoes, to cook over after fuel ran out.

“We saw fear and hunger and death. I am an old woman and I have never seen anything like this.”

The Sunni Muslim militants seized Mosul in a shock offensive across northern and western Iraq in 2014 but have lost much of that territory to resurgent government forces in the past year. The campaign to recapture the city, Iraq’s second largest, began last October.

Defeat in Mosul, the militants’ last urban stronghold in the country, would still leave Islamic State in control of swathes of Syria and Iraqi territory near the Syrian border.