They met hours after NATO airstrikes battered Gadhafi's tanks, helping Libyan rebels push back government troops that had been advancing quickly toward the opposition's eastern stronghold.
The terms of the African Union's road map were unclear, such as whether it would require Gadhafi to pull his troops out of cities, as rebels have demanded.
"We have completed our mission with the brother leader, and the brother leader's delegation has accepted the road map as presented by us," said South African President Jacob Zuma. He traveled to Tripoli with the heads of Mali and Mauritania to meet with Gadhafi, whose more than 40-year rule has been threatened by the uprising that began nearly two months ago.
"We will be proceeding tomorrow to meet the other party to talk to everybody and present a political solution," Zuma said. He called on NATO to end airstrikes to "give the cease-fire a chance."
Gadhafi has ignored the cease-fire he announced after international airstrikes were authorized last month, and he rejects demands from the rebels, the United States and European allies that he relinquish power immediately.
Gadhafi enjoys substantial support from countries of the AU, an organization that he chaired two years ago and helped transform, using Libya's oil wealth. So it is not clear whether rebels would accept the AU as a fair broker.
Though the AU has condemned attacks on civilians, its current leader, Equatorial Guinea President Teodoro Obiang Nguema, decried foreign intervention in Libya, calling the uprising an internal problem.
A rebel battlefield commander said four airstrikes yesterday largely stopped heavy shelling by government forces of the eastern city of Ajdabiya -- a critical gateway to the opposition's de facto capital of Benghazi. NATO's leader of the operation said the airstrikes destroyed 11 tanks near Ajdabiya and another 14 near Misrata, the only city rebels still hold in the western half of Libya.
Sunday's fighting in Ajdabiya killed 23 people, 20 of them pro-Gadhafi forces, said Mohammed Idris, the supervisor of a hospital in the city.