Nkunda, whose forces have routed government troops and gained swathes of territory in North Kivu province in the east of Democratic Republic of Congo since launching a new offensive in August, has repeatedly demanded negotiations.
He said he had been told by Obasanjo that Kinshasa had accepted the principle of talks.
"I know that [the government] has no capacity to fight, so they have only one choice - negotiations," Nkunda said.
"We asked for a response as to where, when, and with whom we are going to do these talks. For us, we propose Nairobi and for the mediator we proposed Chief Obasanjo."
'Relationship of trust'
Video footage of the meeting provided by the UN peacekeeping mission in Congo, MONUC, showed Obasanjo criticising Nkunda for recent hostilities, including Thursday's capture of the town of Ishasha, on the border with Uganda.
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"What has happened in the last 14 days has not made me happy"
Olusegun Obasanjo, UN special envoy to DR Congo
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"What has happened in the last 14 days has not made me happy," Obasanjo said, rising to his feet to address Nkunda, who remained seated at a low table.
"I tried to build a relationship of trust, but I don't receive the same from you."
Obasanjo said Nkunda should have informed him he was planning fresh offensives.
"You are making me a laughing stock," he said.
Nkunda said the ceasefire he had declared applied only to fighting against the Congolese army, not against what he described as "foreign negative forces".
That ceasefire has brought nearly two weeks of relative calm but his men have continued attacking Congolese and Rwandan militias allied with the government.
Talks rebuffed
Obasanjo was in Congo on his second mission in two weeks to try to end the fighting in North Kivu that has displaced around 250,000 civilians and at one point brought Nkunda's troops to within 10 km of the provincial capital, Goma.
The envoy, who met President Joseph Kabila in the mineral-rich African country on Friday, has pressed for talks.
Government ministers this week rebuffed the possibility of direct negotiations with Nkunda, calling for him to return to an earlier peace pact signed in January.
Emerging from his one-hour meeting with the rebel leader, Obasanjo avoided questions.
"We have advanced the course of peace," he said.
MONUC said clashes between Nkunda's National Congress for the Defence of the People (CNDP) and armed groups erupted for a second day near Masisi town on Saturday.