Several dozens were killed and hundreds wounded in the recent gun battles in Mogadishu.
In an unprecedented statement, 39 aid agencies also said they were unable to effectivly respond to the growing "humanitarian catastrophe" in Somalia, caused by insecurity in the country.
The UN said: "Of the people who have left the capital since Saturday, about 46,000 have settled along the road linking Mogadishu to Afgooye, some 30km west of Mogadishu."
"Another 42,000 have either fled Mogadishu for areas outside the city or moved to safer neighbourhoods within the capital", the UN said.
Somalia has been in crisis since 1991. An interim government, backed by the UN, has failed to establish security thoughout the country.
Nearly half a million people were displaced from Mogadishu after fighting earlier in the year.
Hundreds of thousends of refugees are now living in tiny huts and on roadsides.
Catherine Weibel, a spokeswoman for the UN High Commission for Refugees in Somalia, told Al Jazeera: "It remains very difficult for humanitarian agencies to access Mogadishu because of insecurity and even because of the numerous checkpoints along the roads."
"We still have the possibility of accessing Afgooye. We have already helped about 80,000 people earlier this year in Afgooye and we are preparing to do another distribution to the new arrivals," Wirbel said.
"The only solution to really help people efficiently would be an understanding between the political parties."