The CNDP said on Tuesday that it had decided a "unilateral and immediate pull back" to create "separation zones" between themselves and government forces in North Kivu province.
Its deputy chief of staff was due to meet the DR Congo's national army land forces commander on Wednesday near Rwindi, where well-armed rebel fighters have pushed back the demoralised DR Congo army in recent days.
However, thousands of people continued to flee the fighting which flared up several weeks ago, with the UN High Commissioner for Refugees on Wednesday reporting a new influx into neighbouring Uganda.
"There was an influx of 2,000 people who crossed into Ishasha last evening [Tuesday]," Roberta Russo, UNHCR's spokeswoman in Uganda, said.
More than 14,500 people are believed to have arrived in the region since August.
Most of the Congolese in Ishasha wanted to be transported to the Nakivale, a large refugee camp in Uganda's Mbarara district, Russo said.
More than 250,000 people are estimated to have been displaced by the fighting, which has also left at least 100 civilians dead and is threatening to cause a humanitarian crisis.
Malnutrition in some areas of North Kivu province has risen ten-fold, according to US-based aid organisation World Vision.
"The conflict has intensified the effects of poverty 10 times over and the situation has become dire," Suzanne Kahamba, a World Vision aid worker and nurse, said.
"But I fully believe that if there is peace ... people will be able to go home, farm their land and look after their families."
World Vision said before the conflict intensified, two children arrived every day on average at a World Vision nutritional centre east of the town of Rutshuru, but the number had gone up to between eight and 10 now.
Kabila's government and its Western allies have been struggling to put together a national army from the patchwork of central army soldiers and former rebel factions that fought in Congo's 1998-2003 war, which sucked six African states into the conflict.
DR Congo's North Kivu conflict traces its origins back to Rwanda's 1994 genocide, when Hutu militias killed about 800,000 Tutsis and moderate Hutus before fleeing into eastern Congo.
Olusegun Obasanjo, the UN envoy and former Nigerian president who met Nkunda on Sunday, said the rebel leader had agreed to take part in peace talks in Nairobi, Kenya.
Kabila has not confirmed he is ready to meet Nkunda face to face.