The IS jihadists seized the Iraqi city, the capital of Iraq's largest province, Anbar, earlier this week, marking their most significant victory since mid-2014.
Adrian Edwards, spokesman for the UN refugee agency, said some 128,000 people had fled the restive Ramadi district since the beginning of April.
"Then another 55,000 or so (have fled) since the second flare-up of conflict earlier this month," he told reporters.
He said that around 90 percent of those who had fled since the IS offensive began remained in Anbar province.
Just two days ago the International Organization for Migration put the number of people displaced from Ramadi since May 15 at 40,000.
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The jihadist surge, which also saw them capture the ancient Syrian city of Palmyra this week, comes despite eight months of US-led air strikes aimed at pushing them back.
It has sparked an exodus of tens of thousands of fearful civilians in both countries and raised fears that the jihadists will repeat in Palmyra the destruction they have already wreaked at ancient sites in Iraq.
The UN human rights agency said Friday it had received "credible reports" that around one third of Palmyra's estimated 200,000 inhabitants had fled.
As the crisis in the region intensified, the UN's World Food Programme warned it was running out of cash to help displaced people in Iraq not living in camps.
"Due to significant funding shortfall, WFP Iraq has reduced since April the size of the monthly family food ration for displaced families," spokeswoman Elisabeth Byrs told reporters, adding that rations now meet just 40 percent of nutritional needs, down from 80 percent.
"WFP urgently needs $108 million to continue its operations in Iraq up until October this year," she said.