Forces led by Syria's government have seized at least 75% of eastern parts of the city from rebels in recent weeks.
Tens of thousands of civilians have fled those districts, with more than 8,000 leaving during a humanitarian pause on Thursday.
Rebels were also reportedly stopping people from leaving, the UN said.
At a briefing in Geneva, Rupert Colville, the spokesman for the UN High Commissioner on Human Rights, said up to 100,000 people were trapped in "ever-shrinking" areas of eastern Aleppo.