The ISIS militants seized the Iraqi city, the capital of Iraq’s largest province Anbar, on May 17, marking their most significant victory since mid-2014.

William Spindler, spokesman for the U.N. refugee agency, said around 85,000 people had fled the violence in Ramadi since mid-May, and more than 180,000 had been displaced from the city and surrounding area since early April.

A week ago, the U.N. said 55,000 people had fled Ramadi since May 15.

Spindler told reporters in Geneva that restrictions placed on people fleeing the fighting by Iraqi authorities were forcing many to remain in conflict areas.

“Many people are still on the move,” he said, adding that UNHCR and other aid organisations were struggling to locate them.

The surrounding provinces of Babylon and Kerbala had been closed to displaced people from Anbar, and around 85 percent of those who have fled Ramadi remain inside Iraq’s largest province, he said.

Thousands of people who fled the militants’ takeover of Ramadi had remained stuck at Bzeibez bridge for days as the bridge was closed.

The floating bridge, which connects Anbar to Baghdad or other areas where displaced people have sought shelter further south such as Hilla and Najaf, was open Tuesday.

Spindler said the bottleneck at the bridge had eased, but that “the requirements for displaced people to have a local sponsor in Baghdad (to cross) remains a concern.”

“It hampers swift access to safety, leaves people waiting in searing heat without proper shelter and makes the displaced vulnerable to exploitation,” he warned.

Strict requirements for other documentation has hiked the difficulties of reaching safety further.

“Our partners have spent days helping 600 vulnerable people, many with disabilities or serious medical conditions, get access to Baghdad governorate,” Spindler said.

Aid workers had among other things been forced to help displaced people return to Amriyat Al-Fallujah hospital to get required medical certificates to prove they met the requirements for entry, as authorities were only allowing people in need of medical care into Baghdad.

“UNHCR is urging the authorities to address this problem and more broadly to ensure freedom of movement,” he said.