The fresh clashes happened at the villages of Katoro and Nyongera, near Kiwanja in Nord-Kivu province, a security source at Kiwanja who asked to remain anonymous said.
The source said that as well as the rebels and the Mai-Mai militia, the fighting might also involve Government troops and possibly Rwandan Hutu rebels.
"The CNDP are trying to dislodge us from Katoro," said Mai-Mai spokesman Didier Bitaki of Nkunda's National Congress for the Defence of the People.
CNDP spokesman Bertrand Bisimwa said the use of heavy weapons meant that Government troops and Rwandan Hutu rebels were involved in the fighting. The Hutu force was fighting alongside the government soldiers, he said.
"They tried to advance on our positions at around 6:30am (local time) to take Kiwanja," said Bisimwa. "Our forces are currently resisting them."
Kiwanja, 75 kilometres north of the provincial capital of Goma, was the scene of fierce clashes earlier this month during which at least 50 civilians were killed. Human Rights Watch, citing civilians, blamed Nkunda's for most of the killings.
The fighting came just a day after Nkunda's rebels pulled back from two other fronts in Nord-Kivu, at points away from the current fighting.
- Australian Broadcasting Corporation
- © ABC