Nearly a week after the Islamic State (IS) captured the Iraqi city of Ramadi, the plight of tens of thousands who fled the extremist group has yet to be resolved. The Iraqi government continues to prevent most from entering Baghdad, where their safety would be best assured, and locals and aid workers say continued IS offensives in Anbar Province, of which Ramadi is the capital, risk putting the lives of those fleeing in even greater danger.

According to the International Organization on Migration, some 40,000 people fled Ramadi as Iraqi Security Forces fled the city on Sunday in the face of an assault by militants with IS.

Speaking to VICE News Friday evening, Lise Grande, the UN's humanitarian coordinator in Iraq, said most of those fleeing Ramadi have not entered Baghdad, and that the total number of displaced people in Anbar has risen to include those fleeing other cities and towns near Ramadi.

Grande said 24,000 people — like all the UN's current figures, a rough, preliminary estimate — were seeking shelter in the city of Habbaniyah, less than four miles from an airbase where thousands of Shia militiamen are reportedly gathering in preparation to assault Ramadi. About 12,400 people, said Grande, were in Amiriyat Fallujah, a town just 18 miles southeast of IS-controlled Fallujah, and 5,000 reportedly remained at the entrance to the Bzeibez floating bridge that separates Anbar province from Baghdad.

On Wednesday, Iraqi authorities allowed a reported 2,000 people to cross, but as of Friday night, the bridge had been completely shuttered, leaving families to fend for themselves with little or no protection amid soaring daytime temperatures and a vicious sandstorm. The UN reported several had died while waiting to be allowed across the bridge.

"There are a number of people who have died there, the conditions are horrible," Grande said.

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The Shia-led government has expressed concern that IS infiltrators could be among those seeking to enter Baghdad, and have required that families prove they have a sponsor inside the capital before proceeding. The same conditions, the UN reported Friday, are applied to those attempting to enter Karbala and Babylon. Most of those displaced in Anbar are Sunni Muslims.

"They are screening families because they want to make sure hostile elements do not enter the city," said Grande.

Other aid workers confirmed the dire state of affairs at the Anbar side of the Bzeibez bridge.

"This checkpoint is officially closed by the authorities," Salah Noori, Baghdad chief at the Norwegian Refugee Council, told VICE News. "We don't know what will happen in the next couple of days as we are expecting more and more internally displaced people, and a new wave of displacement to this location."

Grande said an additional estimated 5,400 people had congregated in Khalidiyah, along the Euphrates River and just two miles from Habbaniyah, and where IS militants attacked last night.

"Those people are running, plus local families are running, for their lives," said Grande.

Also overnight, Sunni extremists captured the town of Husseiba, some four miles east of Ramadi, after tribal and police forces retreated.

Noori said thousands of those seeking safety did not have sponsors in Baghdad, and others were fearful for their own security inside the city.

"The situation is critical for these IDP families," Noori said, adding he was "extremely concerned about the restrictions on movement."

Those who have been allowed into the capital, said Noori, have "very limited access to basic services," and "are living in unfinished buildings, tents, and other inadequate shelter arrangements."

Even if those driven away by IS eventually reach safer areas, aid workers report funding and supplies to deal with the catastrophe are dangerously low. The UN says it will run out of emergency kits in two weeks, and that by June it will have to close 77 health facilities across Iraq. In July, without further financing, the UN will no longer be able to feed any of the more than 2.5 million Iraqis it currently offers assistance to.

The 40,000 people who fled Ramadi in the last week join more than 130,000 that were displaced from the city in mid-April. Grande said about half of those displaced eventually managed to enter Baghdad. Others were able to reach other provinces or Kurdish controlled areas.