The two sides have been holding direct talks in the Kenyan capital since Monday in a bid to agree a framework deal for substantive negotiations to end months of fighting in eastern Democratic Republic of Congo.
More than 250,000 people have been displaced by the fighting in eastern North Kivu province since August 28.
Obasanjo said late on Wednesday that the discussions had stalled over the rebels' insistence on broadening negotiations to include the situation in the whole of DR Congo, not just the east, of which a vast swathe is under rebel control.
He identified another stumbling block as a lack of decision-making authority on the part of the rebel delegation representing the National Congress for the Defence of the People, the group led by Laurent Nkunda, the renegade general.
Bertrand Bisimwa, a spokesman for the CNDP told the AFP news agency earlier on Thursday that the rebel delegation was prepared to continue talking, despite their threat to quit the night before, after accusing Obasanjo of being biased towards the government.
"We have a full mandate to negotiate ... while the government delegation has not," said Bisimwa, angered at what he said was an attempt by Obasanjo to sideline the rebel delegation.
Obasanjo said Wednesday that his mandate as special envoy of the UN Secretary General did not extend to discussing the global situation in the vast, mineral-rich central-African country.