Rwanda has sent at least 5,000 soldiers into neighbouring DRC as part of the operation launched on Tuesday to track down Hutu FDLR rebels.
Nkunda's arrest marked a striking turnaround, with Rwanda having previously been accused of supporting Nkunda in his campaign against the Kinshasa government, raising fears of a regional conflict.
Rwanda has in turn accused DRC of sheltering the FDLR. That group includes some of the main perpetrators of the 1994 Hutu genocide in Rwanda which saw the slaughter of 800,000 Tutsis and moderate Hutus.
Nkunda's capture and the joint operations against the FDLR signal shifting alliances in the conflict-torn east and tighter cooperation between former rivals Rwanda and DRC.
The ex-general remained in Rwanda on Saturday, a DRC government spokesman said, with Kinshasa seeking his extradition.
Lambert Mende, a DRC government spokesman, said on Saturday that Nkunda was held in Gisenyi, across the border in Rwanda.
Nkunda was captured after fleeing to Rwanda to escape the joint operations after his position was fatally weakened and lost the support of top commanders who switched allegiance to the government earlier this month.
Territory once held by Nkunda has returned to government control, including Rutshuru, once considered the rebels' "capital."
Save The Children said in a statement that Nkunda's arrest could see 1,500 child soldiers released.
Nkunda could face the death penalty if extradited and convicted in DRC.
"The war is over, that is the message of President [Joseph] Kabila," Norbert Basengezi Katitima, the Congolese agriculture minister, said as he and other officials made a symbolic visit on Saturday to eastern Rutshuru, held until recently by Nkunda's men.
Charles Mwando Nsimba, the DRC defence minister, also told the gathered crowd that Rwandan troops "are not in Nord-Kivu to occupy us, but to help us restore peace."
The Rwandan army twice occupied eastern Congo in the 1990s in its battle against the FDLR, and its return has sparked alarm among local inhabitants, aid agencies and the UN peacekeeping force MONUC.
The FDLR has thrived in eastern Congo, where armed groups have effectively been proxies of Rwanda and DRC.
A number of them have holed up in Marangara, a small eastern village, a Hutu militia leader told a reporter.
"The Tutsis of Kagame can attack at any moment. We are deployed in combat position throughout the forest," he said.
Rwandan soldiers were stationed less than 10km away in the strategic location of Tongo.