UN peacekeepers had gone to the area to try to halt the fighting.
Nkunda said later on Wednesday that his forces from the National Congress for the Defence of the the People (CNDP) were observing the ceasefire around Goma, the provincial capital, where thousands of refugees are sheltering in relief camps.
"It [the ceasefire] is still being maintained," Nkunda told Reuters by telephone from headquarters in North Kivu.
Aid workers seeking to locate and help thousands of displaced civilians in the Rutshuru area said they had been forced to suspend operations there because of the hostilities.
"We left Rutshuru yesterday because of the fighting in the area. When the situation improves, we hope to return and continue our programmes, but at present we can't," Francis Nakwafio Kasai, a UN humanitarian agency (Ocha) official, said.
The enduring conflict in eastern Congo, which persists years after the end of a wider 1998-2003 war, has triggered international efforts to secure peace on the country's Great Lakes border with Rwanda, Uganda and Burundi.
Kenya announced on Wednesday that a summit of Great Lakes region heads of state, which would bring together the Congolese and Rwandan presidents, Joseph Kabila and Paul Kagame, would be held in Nairobi on Friday.
The conflict is fuelled by ethnic hatred left over from Rwanda's 1994 genocide.
Nkunda claims the Congolese government has not protected ethnic Tutsis from the Rwandan Hutu militia that escaped to Congo after helping slaughter a half-million Rwandan Tutsis in the Rwanda massacres.
Nkunda, who defected from the army in 2004, now says he is fighting to liberate all of Congo from a corrupt government.
He went on the offensive on August 28 and brought his fighters to the edge of Goma last week before declaring a unilateral ceasefire.
Congo and Rwanda have accused each other of supporting feuding rebel and militia groups.