The report, by the UN Office for the Coordination of Humanitarian Affairs, said roads had been blocked and tanks were on the streets. Some of the fiercest fighting was in the diplomatic area near the UN compound.
The Red Cross estimates that at least 125 people have been killed and more than 230 people injured since clashes broke out on Friday.
The UN Humanitarian Coordinator in Yemen, Jamie McGoldrick, called for a humanitarian pause on 5 December to allow civilians to leave their homes and seek assistance, and for aid workers to continue life-saving programmes.
"They dont know whats coming next... Children and young people - its terribly sad," he told the BBC.
"And for us were in the situation we cant help them because were equally locked down and we have not got the ability to address their needs the way we should."