"We will not accept outsiders coming in to provide security for us here," he said.
"Either you help us in the revolution or you keep quiet with Monuc. But if you wait for Monuc to bring you peace, you can wait forever."
"We must unite to work to ensure our security. Every day you ask for something more, but how long will you go on begging?" Nkunda said, urging the region's disparate ethnic groups to "cohabit" peacefully.
"There is only one solution, that we co-exist peacefully," he said. "There is enough place for even foreigners."
Nkunda's fighters withdrew from two key frontlines in North Kivu this week, ostensibly to boost a peace mission by Olusegun Obasanjo, the UN special envoy to Congo, who is seeking to end the conflict and the ensuing humanitarian disaster.
But they remain poised outside Goma, where the conflict is centred.
Obasanjo was due to return to Congo next Saturday, Nkunda said, but the UN did not immediately confirm the claim.
The UN peacekeeping force has been criticised for failing to protect the estimated 250,000 people displaced by the fighting, and atrocities by both the rebels and government forces.
With the UN Security Council on Thursday having approved 3,000 reinforcements for Monuc, a Kinshasa government spokesman urged a new approach.
Many armed groups, pro-government militias and rebels, operate in the unstable region which borders on North Kivu, scene of fighting for nearly three months between the army and Nkunda's rebels.
The Monuc said there was a lull in fighting for a second straight day on Saturday with no incidents reported in North Kivu.