Mr Obasanjo is mediating between Mr Nkunda and the government
DR Congo rebel leader Laurent Nkunda has told UN peace envoy Olusegun Obasanjo he will support a peace process with the government.
Gen Nkunda also said he would respect a ceasefire if the Congolese government did. Mr Obasanjo said it would take effort from both sides to keep a truce.
The rebel agreed to cease-fire monitors as long as they did not include UN peacekeepers, whom he accuses of bias.
The meeting came amid reports of fresh clashes in the east of the country.
An estimated 250,000 people have been made homeless by weeks of conflict between rebels and government troops.
The government of DR Congo's President Joseph Kabila has to date rejected rebel calls for direct negotiation.
After his meeting with Gen Nkunda in the rebel-held town of Jomba, Mr Obasanjo left for Kigali in neighbouring Rwanda which the DR Congo government accuses of supporting the rebellion.
BBC world affairs correspondent Mark Doyle reports from Goma that Gen Nkunda's support for a ceasefire is not new and some observers were surprised at how Mr Obasanjo appears to have been seduced by a man Congolese officials and human rights groups refer to as a "war criminal".
It may be that Mr Obasanjo was expecting the rebel group to be a motley collection and when he saw that Mr Nkunda's troops were a well-equipped military unit, he was surprised, our correspondent adds.
'Two to tango'
Speaking after the talks , the rebel leader - wearing a grey suit rather than a military uniform - acknowledged that many lives had been lost in the fighting.
An estimated 250,000 people have been made homeless by the fighting
"Today is a great day for us because we were losing many men and now we have a message of peace. We should work with this mission," he said.
"We agreed to open humanitarian corridors to support the process."
Gen Nkunda says he is fighting to protect his Tutsi community from attacks by Rwandan FDLR Hutu rebels who fled to DR Congo after the 1994 genocide.
Mr Obasanjo, Nigeria's former president, told reporters the discussions had gone "extremely well".
But he suggested concerted efforts would be needed: "It's like dancing the tango: you can't do it alone."
Mr Obasanjo, who met President Kabila on Friday, said the president had not laid down conditions for talks with the country's rebels.
The UN envoy also met members of DR Congo's parliament and ambassadors representing UN Security Council members in Kinshasa on Saturday.
In the latest clashes on Sunday, witnesses reported hearing artillery, rockets and small arms fire near the village of Ndeko, about 55 miles (90km) north of provincial capital Goma and near the strategically important town of Kanyabayonga.
UN peacekeepers protected a convoy delivering aid to eastern areas
A UN military spokesman said soldiers from Gen Nkunda's rebel force and Congolese army troops had been involved in the fighting.
In a recent BBC interview, Gen Nkunda said he wanted to take over the whole of Congo.
This was obviously propaganda, our correspondent says, but it scared many Congolese people because they, on the whole, believe that Gen Nkunda is backed by Rwanda which, though small, is powerful.
Rwanda, for its part, says Congo backs an anti-Rwandan government militia force based in the Congolese forest, our correspondent adds.
The UN says the conflict that began in August between Gen Nkunda's fighters and government forces has caused a humanitarian catastrophe.
On Friday, for the first time after weeks of fighting, UN aid workers delivered maize and lentils to some of the 50,000 or more hungry civilians in Rutshuru territory, north of Goma.