At least 20,000 people are sheltering at two UN bases in the capital Juba, while 17,000 are sheltering in the UN base in the rebel-held town of Bor, state capital of powder-keg eastern Jonglei state.
A further 7,000 people are sheltering at the UN base in Bentiu, state capital of the oil-producing Unity state -- also in rebel hands -- the UN added, while "sporadic fighting" has been reported in Upper Nile, another oil-rich state.
The UN said at least 45,000 people were sheltering at those and other bases.
"The estimated number of people displaced in the current crisis in South Sudan has risen to 81,000," the UN Office for the Coordination of Humanitarian Affairs (OCHA) said in its latest situation report.
"Given the limited access to civilians outside population centres, the number is likely to be significantly higher."
The official toll is 500 dead, although the real figure is believed to be far higher, aid workers say. Hundreds of thousands of others are believed have fled to the countryside, prompting warnings of an imminent humanitarian disaster.
"There are credible reports of grave abuses committed against civilians in different parts of the country, including killings," the UN added.
The town of Bor, located just 200 kilometres (125 miles) north of Juba, is an area of special concern, with the army saying it is preparing to launch an assault to recapture it since they lost control on Wednesday.
"In Bor, the situation for the 17,000 people sheltering at the base is challenging, the lack of food and shelter is becoming urgent," the UN said, warning that there has been "large-scale looting of humanitarian compounds and civilian property" in the town.
"The situation in Jonglei deteriorated further, with reported clashes between different armed factions south of Bor... the base is being reinforced with additional protective barriers, including the area hosting the displaced civilians," it added.