Congolese government forces were also preparing to expand their military operations against militia groups in the region.
Colonel Delphin Kahimbi, operations commander of government forces in North Kivu, said on Sunday a local Mai Mai militia group, which says it is working alongside the army, was in fact hindering his plans to deal with Nkunda, and that he was now ready to act against them too.
He gave the group 48 hours to go to army integration centres and disarm or face military action.
A Mai Mai assault during the weekend on rebel-held Bunagana, a border town on DRC's eastern frontier with Uganda, triggered a series of counter-attacks by Nkunda loyalists against government troops.
"I received the order to give them 48 hours," Colonel Kahimbi said, adding he was ready to act against the Mai Mai.
"With the time needed to prepare, I think we can get on with it by Wednesday morning," he said.
Kasereka Kabamba, a former senior army officer leading the Mai Mai militia group, rejected that ultimatum on Monday, saying Nkunda's men must lay down their weapons first.
"If Nkunda chooses to go to the centres, then we go," he said. "If we go first, he can go on killing our people."