Obasanjo met Joseph Kabila, the country's president, in a bid to stop fighting between government troops and rebel forces.
After meeting Kabila in the capital Kinshasa, Obasanjo, a former Nigerian president, travelled to Goma, the provincial capital of North Kivu, where he said he would hold talks with Nkunda, who heads the National Congress for the Defence of People (CNDP).
Obasanjo said earlier on Saturday that Nkunda had telephoned him last week and "explained that he is full of expectations for us to meet and talk face to face".
"Nobody can say for certain what he wants ... but I will get authentically from him what he wants," Obasanjo said.
Bertrand Bisimwa, a spokesman for the CNDP, said a meeting between Nkunda and Obasanjo had been planned and should take place later on Saturday or on Sunday.
Obasanjo could see Nkunda in the rebel stronghold of Rutshuru, about 75km of Goma, he added.
Fighting between the army and fighters loyal to Nkunda, who claims to be fighting to protect ethnic Tutsis in the region, has displaced at least 250,000 people.
At least 100 people have been killed since fighting broke out in September, despite the presence of about 17,000 UN troops - the largest UN peacekeeping force in the world.
Obasanjo's diplomatic mission comes amid reports of renewed fighting between government troops and rebel fighters in Kabasha, a village around 110km north of Goma.
Colonel Jean-Paul Dietrich, a UN spokesman, said the exchange of fire lasted for about 10 minutes and that it was "not clear who started it".
He said UN peacekeepers had launched patrols in the area.
On Friday, Obasanjo met Jose Eduardo Dos Santos, the Angolan president, who assured him no Angolan troops were in DR Congo, despite numerous reports of Angolans helping Congolese forces.
There are fears the country could slide back into a ruinous war such as the one in 1998-2002, that drew in more than half a dozen African nations and reduced DR Congo to rival fiefdoms.
Fighters backed by Uganda and Rwanda seized vast swaths of territory rich in coffee, gold and tin in the east. Angola and Zimbabwe sent tanks and fighter planes to back DR Congo's government in exchange for access to lucrative diamond and copper mines to the south and west.
Eastern Congo has been unstable since millions of refugees spilled across the border from Rwanda's 1994 genocide, which saw more than 500,000 ethnic Tutsis and moderate Hutus slaughtered.