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 U.S. and its 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, last week its current leader, Equatorial Guinea President Teodoro Obiang Nguema, decried foreign intervention in Libya's nearly two-month-old uprising, which he declared to be an internal problem.
An official from the African bloc, Khellaf Brahan, said previously that its proposals call for an immediate cease-fire, opening channels for humanitarian aid and talks between the rebels and the government.
Through the rebels have improved discipline and organization, they remain a far less powerful force than Gadhafi's troops. Members of the international community have grown doubtful that the opposition can overthrow Gadhafi even with air support, and some are weighing options such as arming the fighters even while attempting diplomatic solutions.
A rebel battlefield commander said four airstrikes Sunday 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.
NATO is operating under a U.N. resolution authorizing a no-fly zone and airstrikes to protect Libyan civilians.
The fighting in Ajdabiya on Sunday killed 23 people, 20 of them pro-Gadhafi forces, said Mohammed Idris, the supervisor of a hospital in the city. A total of 38 people were killed in fighting over the weekend, including 11 rebels and seven civilians, Idris said.
The main front line in Libya's uprising runs along a 600-mile (1,000-kilometer) coastal highway from Benghazi, Libya's second-largest city, to Tripoli, the capital, where Gadhafi's power is concentrated. Rebels have been pushed back on two previous advances toward Tripoli, both times as they approached the heavily fortified Gadhafi stronghold of Sirte.
Over the past few days, Gadhafi's forces have been knocking the rebels back eastward in their most sustained offensive since international airstrikes drove them back last month. If they had taken Ajdabiya, they would have had a clear path to opposition territory including Benghazi, about 100 miles (160 kilometers) away along the coast.
"If he controls Ajdabiya, he makes us feel like we are unsafe because he can move anywhere in the east," said Col. Hamid Hassy, the rebel battlefield commander.
Western airstrikes, initially conducted under U.S. leadership, began on March 19 to repel Gadhafi's forces just as they were at the doorstep of Benghazi.
Hassy said Gadhafi's forces fled the western gate of Ajdabiya and by mid-afternoon had been pushed back about 40 miles (60 kilometers) west of the city. However, sporadic shelling could still be heard around western Ajdabiya.
A body brought to the morgue, said to be a rebel fighter shot near Ajdabiya's west gate, had his hands and feet bound. Another body was an Algerian who had been fighting for Gadhafi, Dr. Suleiman Rafathi said at the hospital. He said the man's ID confirmed his origin, but that rebels took the ID before an Associated Press reporter arrived. Rebels have said many Gadhafi fighters are foreign mercenaries.
Another Gadhafi fighter, about 20 years old, was on a ventilator -- brain-dead but with a beating heart, Rafathi said.
Rebel fighter Sami Kabdi said the young man had been firing out a window of a school. When rebels told him to surrender, he put the muzzle of his AK-47 under his chin and fired, Kabdi and Rafathi said.
Rebels had been growing critical of NATO, which accidentally hit opposition fighters in deadly airstrikes twice this month. They have complained that the alliance was too slow and imprecise, but Hassy, the rebel commander, said it is getting better.
"To tell you the truth, at first NATO was paralyzed but now they have better movement and are improving," he said.
The commander of the NATO operation, Canadian Lt. Gen. Charles Bouchard, stressed in a NATO statement that the point of the airstrikes was to protect civilians, not to work hand-in-hand with the rebels.
"The situation in Ajdabiya, and Misrata in particular, is desperate for those Libyans who are being brutally shelled by the regime. To help protect these civilians we continued to strike these forces hard," Bouchard said.
NATO noted that it is enforcing the no-fly zone on both sides, having intercepted a rebel MiG-23 fighter jet that it forced back to the airport Saturday.
In the embattled city of Misrata, the lone rebel outpost in the west of the country, residents said shelling continued Sunday, killing one and wounding two others seriously.
"We woke up at 7 a.m. from the tank fire," said a doctor working at the local hospital who spoke on condition of anonymity for fear of reprisal.
Libya's third-largest city has been pounded without cease for more than a month by Gadhafi's heavy weapons, but the rebels have managed to hold out.
In Tripoli, Libya's deputy foreign minister accused NATO of a double standard on the no-fly zone, claiming that government forces shot down two U.S.-built Chinook helicopters being used by rebel forces in the east of the country.
"We have a question for the allied forces -- is this resolution made for the Libyan government only or everyone in Libya?" he asked.
The report could not be confirmed with the rebels, but journalists in the area did describe seeing at least one helicopter apparently fighting for the rebels in the area Saturday, though it lacked the distinctive double rotor design of the Chinook and appeared to be a Russian-built model.
Abbot reported from Benghazi, Libya.