The Congolese government welcomed the news of Nkunda's arrest by the joint force, which is tasked with hunting down Rwandan Hutu fighters based in DR Congo.
"Talks are under way ... I am sure that today the government of Congo will connect with the government of Rwanda to see how Nkunda can be presented to Congolese authorities," Mende Omalanga, DR Congo's communications minister, told Al Jazeera.
"When you are implicated in mass killings, such as in the case of Nkunda ... you must respond to the judges of our country."
Kinshasa has an arrest warrant against Nkunda and accuses him of war crimes in the eastern province of South Kivu, which CNDP forces captured in June 2004.
Amini Kakule, a Congolese journalist based in eastern DR Congo, told Al Jazeera that news of Nkunda's arrest came as a surprise.
He said it was not clear yet whether the renegade general would be extradited by the Rwandan government to Kinshasa.
"Nothing has been announced; nothing has been declared at the moment," he said.
Al Jazeera's Yvonne Ndege, reporting from Dungu in eastern DR Congo, said the future for Nkunda "looks very bleak".
"He is in the hands of the Rwandan military who are going to face increasing pressure to hand him over to the Congolese. When that does happen, he will face charges of war crimes in the Congolese capital Kinshasa," she said.
"The evidence against Nkunda is great. I am sure he will be found guilty and he is likely to spend a very long time in prison."
More than 3,500 Rwandan troops have crossed into DR Congo in recent days to work alongside Congolese government forces trying to disarm members of the Democratic Forces for the Liberation of Rwanda (FDLR), another rebel group.
The FDLR, which emerged in the wake of the 1994 genocide of Rwandan Tutsis and moderate Hutus, is commonly seen as the cause of more than a decade of instability in east DR Congo.
The CNDP has in the past claimed that the Congolese government has not done enough to protect Tutsis living in the east of the country.
Late last year, Nkunda led his forces in an offensive against Congolese government forces in North Kivu province.
More than a quarter of a million civilians fled their homes to escape the fighting.
But in recent days several senior CNDP commanders have defected and joined the ranks of Congolese forces, saying that their war against Kinshasa has ended.
Bosco Ntaganda claims to have taken over as the leader of the CNDP and says he has directed his fighters to work alongside the Rwandan-Congolese joint effort against the FDLR.
Fighters loyal to Nkunda, who has not commented on news of last week's defections, have been accused of war crimes by international human rights groups.
Reversal of fortune
Bernard Smith, Al Jazeera's correspondent in the Rwandan capital Kigali, said Nkunda's arrest marked a dramatic reversal in his fortunes.
"This is a man who has fought for the Rwandans and who many had speculated over the years was backed by Rwanda," he said.
"It seems that for many years the Rwandans have been after the Hutu militia who have been hiding in eastern DR Congo since the 1994 genocide in Rwanda. The Rwandans have twice before invaded DR Congo to try to get these Hutus, but were effectively accused of plundering Congolese resources.
"This time, the Rwandan soldiers have gone in with the backing of the Congolese. It seems that the Congolese has said 'Ok, you can come in and try to get these Hutu militia, but we want you to get Nkunda.' Diplomatic circles suggest that Rwanda agreed to do that."