"Everyone concedes now that really it's pointless to continue pursuing a military solution ... The next step is that we are meeting with Mr Nkunda tomorrow," Benjamin Mkapa, a former Tanzanian president travelling with Obasanjo, said.
However, Mkapa said direct talks between Kabila and Nkunda are not yet on the horizon.
"I think it would be very imprudent of him [Nkunda] to ask for direct talks at once," he said. "Dialogue does not necessarily have to start at the top."
Kabila's government insists Nkunda return to a peace agreement he signed in January, along with other armed factions.
The rebel leader says he still adheres to the deal's principles, but takes issue with its implementation.
In the past three days, more than 10,000 Congolese civilians have fled across the border into Uganda to escape the latest fighting in North Kivu's Rutshuru district.
Refugees have reported family members being killed and homes ransacked in the area.
Nkunda, however, denied his forces, which took the border town on Ishasha on Thursday, have broken the ceasefire.
His group claims to protect the local ethnically Tutsi population from Hutu rebels collaborating with the government, some of which they say took part in the 1994 genocide of Tutsis and moderate Hutus in Rwanda.
Tensions bubbled over in August, sparking clashes between rebel and government forces. Congolese troops have been accused of carrying out looting sprees, while the rebels allegedly committed atrocities.
Around 250,000 people have so far been displaced, creating a humanitarian disaster that UN aid workers and peacekeepers are struggling to control.
The United Nations Security Council has authorised sending 3,000 reinforcements to the country, where 17,000 peacekeepers are already based.