Gen Nkunda says he wants to support a peace process
Rebels loyal to Laurent Nkunda in the Democratic Republic of Congo say they are withdrawing from two fronts to create humanitarian corridors.
The news came after the army chief of staff was sacked following the recent rebel advances in the east.
Meanwhile, France has presented a draft resolution to the UN Security Council to strengthen the UN force in DR Congo.
But a commander in the UN mission (Monuc) says he cannot defeat rebels because of his rules of engagement.
General Bipin Rawat, who commands 6,000 troops, told the UK's Daily Telegraph newspaper that his forces were denied any element of surprise by having to go into the jungle with white trucks and white armoured vehicles.
UN troops also have to fire warning shots and shout verbal warnings before engaging the rebels, who are gathered near the town of Goma, he said.
However, US Assistant Secretary of State for African Affairs Jendayi Frazer said the mandate was as tough as it could get.
"Monuc has a Chapter Seven mandate that gives them the authority to protect the civilian population, to protect the peacekeepers themselves and to act very robustly against those negative forces in the Congo," she told the BBC's Hard Talk programme.
At present, there are about 17,000 soldiers and police in DR Congo - the biggest UN force of its kind.
The French resolution - to be voted on next week - would increase the number of UN troops in the country by 3,000.
Clashes between the army and the rebel forces of renegade General Nkunda have driven at estimated 250,000 people from their homes and created a humanitarian crisis.
Col Jean Muhire, a spokesman for Gen Nkunda's CNDP rebels, told the BBC they were withdrawing to allow aid in and show their commitment to peace following a meeting on Sunday with UN envoy Olusegun Obasanjo.
FORCES AROUND GOMA
CNDP: Gen Nkunda's Tutsi rebels - 6,000 fighters
FDLR: Rwandan Hutus - 6-7,000
Mai Mai: pro-government militia - 3,500
Monuc: UN peacekeepers - 6,000 in North Kivu, including about 1,000 in Goma (17,000 nationwide)
DRC army - 90,000 (nationwide)
Source: UN, military experts
The CNDP decided it "must make a unilateral withdrawal of its troops for a distance of 40km (25 miles) on the Kanyabayonga-Nyanzale front and the Kabasha-Kiwanja front," the AFP news agency quotes a rebel statement as saying.
In the rebel-controlled town of Rutshuru, just south of Kiwanja, there is an air of fear as rumours spread about the shooting of several civilians by the rebels, the BBC's Thomas Fessy reports.
Rebels are holding re-education classes for town officials - starting with DR Congo's history from the time of colonisation, he says.
Col Muhire said UN peacekeepers should move into the buffer zone areas to ensure no other force enters territory it leaves.
The BBC's Mark Doyle in eastern DR Congo says that previous rebel offers to withdraw have been reversed, following shooting by government forces or other confusion.
No mention was made of the front line near Goma city, where the two sides are separated by a dormant lava field created by a nearby volcano.
In the latest violence, the rebels took the town of Rwindi, about 125km (75 miles) north of Goma, near Kanyabayonga - a major military base.
The government of President Joseph Kabila has to date rejected rebel calls for direct negotiation.
On Monday, it was announced that Mr Kabila had named navy chief General Didier Etumba Longomba as the new head of the armed forces.
Correspondents say General Longomba takes responsibility for a badly paid force with low morale and will need to instil discipline.
An estimated 250,000 people have been made homeless by the fighting
The BBC African Service's Kassim Kayira says the army shares the blame for atrocities against the population it is meant to be protecting.
As they have retreated from Gen Nkunda's fighters in recent days, army soldiers looted shops and homes and raped women.
A military tribunal in Goma has sentenced 11 soldiers to life in prison for rape and looting. Another 12 soldiers face court martial in the coming week - one accused of killing a family of six in Goma on 29 October.
Gen Nkunda says he is fighting to protect all minorities, in particular his Tutsi community, from attacks by Rwandan FDLR Hutu rebels who fled to DR Congo after the 1994 genocide.
The Congolese army has been accused of working with the FDLR fighters to exploit eastern DR Congo's rich mineral resources.
The DR Congo government says Gen Nkunda is backed by neighbouring Rwanda - a charge denied by Rwanda's government.