Rene Abandi, a rebel spokesman, said the fighters had resisted an army advance and fought to protect civilian refugee populations in the Kirolirwe and Kitchanga areas, controlled by the fighters.
The rebel strongholds are about 50 to 70km from the provincial seat of Goma.
Humanitarian and military sources say the rebels are recruiting fighters from the Kirolirwe camp.
The latest outbreak of violence began with an army offensive against the rebels on Monday and has heightened fears for the welfare of tens of thousands of people already displaced by months of unrest.
Monuc, the UN peacekeeping force in the DRC, established mobile bases at Kirolirwe which houses about 14,000 internally displaced people (IDP), the majority of them Tutsis, and at Kitchanga where another 18,000 IDP's are located.
The roughly 25,000-strong army outnumbers the estimated 4,000 Nkunda loyalists. But Nkunda has so far rejected demands by the government and the UN to disarm.
Nkunda says he is defending local Tutsis against Hutu fighters from neighbouring Rwanda living in the DRC since the 1994 Rwandan genocide.