The fighting erupted in the eastern suburbs of Beni, a city in the troubled North-Kivu province, with residents hearing gunshots and heavy weapons fire.
The province has been plagued by regular flare-ups of ethnic bloodshed, which over the past year has seen a cycle of attacks and reprisal raids between militias.
"The provisional toll is 13 Mai-Mai militants killed, plus six wounded and three dead on the side of the FARDC (the Congolese army)," lieutenant Jules Tshikudi, an army spokesman in the region, told AFP.
The UN mission in DR Congo known as MONUSCO, which says it has deployed peacekeepers to the region, gave a death toll of "nine Mai-Mai killed", spokesman captain Adil Asserhir told AFP, while confirming that the militants have been driven from Beni.
A local civil society leader Gilbert Kambale however warned that "the Mai-Mai are unpredictable" and for city residents it could be "a nightmarish night after the trauma of the attacks."
The army said the confrontation started with an early- morning attack on two of its positions east of the city, claiming the gunmen were from the Mai-Mai militia.