Nkunda launched a rebellion in 2004, claiming to protect ethnic Tutsis from Hutu militias who fled to Congo after Rwanda's 1994 genocide left more than 500,000 Tutsis and others slaughtered. But critics say Nkunda is more interested in power and Congo's mineral wealth than in protecting his people.
Rebel spokesman Bertrand Bisimwa said Tuesday that his group would immediately withdraw 25 miles (40 kilometers) from hotspots around Kanyabayonga and Kiwanja to allow rebels and Congolese army officials to meet Wednesday.
The meeting near Kanyabayonga "will examine the establishment of zones of separation between their two armies, in order to prevent any possibility of confrontation," Bisimwa said in a statement.
Nkunda told U.N. envoy Olusegun Obasanjo on Sunday that he was committed to a cease-fire and U.N. efforts to end the fighting, but his troops have been carving out an even greater territory in the remote hills north of Goma.
The army's disarray is so dire that Congolese President Joseph Kabila has sacked his army chief.
Congo has the world's largest U.N. peacekeeping mission, with 17,000 troops, but the peacekeepers have been unable to either stop the fighting or protect civilians. A draft Security Council resolution, obtained by The Associated Press on Monday, proposed temporarily adding about 3,100 troops and police to the peacekeeping force in Congo.
On Tuesday, soldiers fought with the Mai Mai militia, which normally supports the government. But the militia appeared to be taking advantage of the army's retreat to steal the soldiers' weapons, witnesses said.
"They (Mai Mai) are seeing soldiers fleeing and they want them to leave their arms with them," Bahati Maene, 19, told The Associated Press after fleeing his home Monday night.
Congolese army Lt. Jean-Pierre Lumisa said the fighting with the Mai Mai was an "isolated case."
"They are not our enemies," he said. "They are just difficult to control and coordinate with."
But U.N. peacekeeping spokesman Col. Jean-Paul Dietrich said that the Mai Mai's change of loyalty could be more serious. "It shows that now local militant groups are advancing against the national army," he said.
Nkunda declared a unilateral cease-fire in late October as his fighters swarmed toward Goma, which serves as regional headquarters for the provincial government, the U.N. and aid groups.
Since then, rebels have consolidated their positions, appointing their own local administrators and forcibly recruiting young men and boys to join their ranks, aid workers say.
Although the rebels halted outside Goma, they now control the entire road from Goma to the doorstep of Kanyabayonga.
In a sprawling camp of 19,000 people about 12 miles (20 kilometers) west of Goma, thousands of people lined up for hours for 20-day rations of food: a handful of salt, a few cups of oil and a few (pounds) kilograms of corn flour and beans.
Despite the seemingly meager rations, the crowd cheered when receiving the food from aid workers, pumping the air with their plastic buckets and plastic bags.
But less than a mile (kilometer) away, 35-year-old Mateo Biroto shoveled clumps of sticky black dirt over a rough wooden coffin.
His wife, Rebecca Yalala, had died the day before of complications from diabetes and malaria.
"When she came to the camp, she became very weak," he said, blinking back tears as about 10 congregants sang hymns in front of the woman's unmarked grave. "She became weak because in the camp she didn't have a good life."
"I loved her so much," Biroto said. "For me, she was very, very, very beautiful."