At least five people died in the fighting, the United Nations said.
Gunshots also rang out at a house in Kinshasa, where U.N. officials and ambassadors were meeting with the country's main political rival Vice President Jean-Pierre Bemba. The shots were believed to have been fired by soldiers loyal to President Joseph Kabila.
"The entire CIAT (foreign donors' group) is in Bemba's house having a meeting with him," a U.N. source told Reuters. "Kabila's people are firing on the area."
The violence started Sunday when the provisional results of the July 30 polls showed that neither candidate had won the election outright, Reuters reported.
The results showed that Kabila failed to win a majority, garnering only 45 percent of the 16.9 million votes cast.
Bemba, a former rebel leader, drew heavy support from the west and the capital but came in second with 20 percent, the AP reported.
The remaining votes were divided among 31 other candidates, according to the country's Electoral Commission.
About 70 percent of Congo's 62 million people voted in the election.
On Monday, news outlets reported that the normally bustling capital city was nearly empty.
"It's a dead city. People are afraid to go out and we who live selling from day to day are screwed if no people are out and about," a street vendor told Reuters. "The politicians should let us get on with our lives."
Congolese and international officials hoped July's election would help bring stability and peace to the politically divided nation, where a five-year civil war that ended in 2003 killed more than 4 million people.
But, violence since the vote has marred expectations for peace.
"Yesterday's incident does not bode well for a good climate for a second round of elections," Jason Stearns, an analyst at the International Crisis Group, told Reuters. "It looks to be tense and conflictual."