Threat of 'war'
Skirmishes with government troops have largely stopped since Nkunda, the leader of Tutsis, called a ceasefire two weeks ago. But his fighters have continued to clash with government-allied militias.
Obasanjo has been pressing for direct talks between Nkunda and Joseph Kabila, the president of the Democratic Republic of Congo, but so far these have not taken place.
"Everyone concedes now that really it's pointless to continue pursuing a military solution"
Benjamin Mkapa, former Tanzanian president
On Friday Obasanjo held talks with Kabila in Kinshasa.
"Everyone concedes now that really it's pointless to continue pursuing a military solution," 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."
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, 120km (75 miles) north of regional capital Goma on Thursday, have broken the ceasefire.
Nkunda says the ceasefire does not apply to operations against foreign militia.
His group claims to protect the local 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.
The UN is trying to transfer people to safer locations west of Goma away from the fighting.