The CNDP launched a major offensive in August, which displaced more than a quarter of a million people and raised fears of a wider regional war. Gen Nkunda and his group says they are fighting to protect the Tutsi community from attack by Rwandan Hutu rebels based in DR Congo, some of whom are accused of taking part in the 1994 genocide.
The Congolese government has often promised to stop the Hutu forces from using its territory, but has not done so. However, others see the CNDP as a Rwandan proxy and the biggest reason why DR Congo is yet to benefit from landmark elections in 2006 intended to draw a line under decades of conflict.
Human rights group have accused CNDP forces, along with those of the government, of numerous killings, rapes and torture. Talks in Kenya aimed at ending the conflict became deadlocked last month, with UN mediator Olusegun Obasanjo complaining that the CNDP's negotiators lacked the authority to make concessions.
The decision to remove Gen Nkunda as leader of the National Congress for the Defence of the People (CNDP) reportedly came after a meeting of the rebel group's military high command on Sunday. In a statement sent to the BBC and signed by Brig-Gen Bosco Ntaganda, the rebels' chief of staff, the high command said Gen Nkunda's "bad leadership" and "bad governance" had distracted the CNDP from undertaking its normal activities and was dangerous for the Congolese people.
The high command had also resolved to set up an ad-hoc "transitional council" to run the group until further notice, the statement said. A spokesman for the high command, Kamanzi Desire, said the council would ensure that the peace process continued.
"The new leadership has pledged before CNDP members, the Congolese people and the international community to create favourable conditions for peace to return to eastern DR Congo with the help of the international community and Monuc (UN Mission in the Democratic Republic of Congo)," he told BBC Afrique.
But a spokesman for Gen Nkunda then told the BBC by phone that the rebel leader had not been ousted - and during that phone call what appeared to be the voice of Gen Nkunda could be heard in the background. The general had called a meeting of senior rebel leaders to take place on Tuesday, the spokesman said.
In recent weeks, Gen Nkunda has reportedly been in Rutshuru, a town in North Kivu, along with a battalion of his troops. The reports indicate that a power struggle may be taking place within the CNDP. If the CNDP splits, it could just mean another rebel group is added to a deadly cocktail of armed militias, correspondents say.
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