The IS jihadists 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 UN 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 UN said 55,000 people had fled Ramadi since May 15.
"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 jihadists' takeover of Ramadi had remained stuck at Bzeibez bridge for days as the bridge was closed.
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.
"UNHCR is urging the authorities to address this problem and more broadly to ensure freedom of movement," he said.
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