A journalist stuck inside a United Nations bunker said mortars were being fired around a residence of candidate and former rebel leader Jean-Pierre Bemba.
U.N. peacekeepers said it appeared the fighting was between Bemba's militia and security forces.
Peacekeepers say the fighting started when police tried to disperse a pro-Bemba demonstration.
Protesters set tires on fire, saying there was vote-rigging in favor of transitional President Joseph Kabila.
An official on Bemba's election team, Eve Baz, told VOA her side believes Congolese are being cheated again.
"We want to have a correct election, to have a fair election and transparency in all these operations," she said. "I feel that there is not transparency now, because we have many problems now of our members , of all our representatives in the tally centers."
Results so far of the second round October 29 runoff give Mr. Kabila a huge overall lead, due to a strong advantage in the east, but Bemba still largely dominates in early vote-counting in the west, including in the capital.
First round results in August led to deadly fighting between security guards loyal to the rival candidates. The guards have yet to be reintegrated into a national army.
The international community has paid hundreds-of-millions of dollars for what many analysts call the most important African election since the post-apartheid vote in South Africa in 1994.
United Nations officials say the aim of the election in the vast mineral-rich Congo is to end decades of misrule, corruption and plundering.