A team of African leaders is on its way to Libya to try to negotiate a ceasefire between rebel forces and those loyal to Col Muammar Qathafi.
South African President Jacob Zuma and three other leaders, representing the African Union, have left Mauritania for the Libyan capital Tripoli.
The team will also visit rebel representatives in Benghazi.
Fierce fighting is continuing in Ajdabiya in eastern Libya, with Col Qathafi's forces pushing back rebels.
The African Union (AU) diplomatic mission comprises representatives from five nations and had gathered in Mauritania's capital, Nouakchott.
The mission has called for an 'immediate end' to fighting, 'diligent conveying of humanitarian aid' and 'dialogue between the Libyan parties'.
Agence France Presse news agency said Mr Zuma, and presidents Mohamed Ould Abdel Aziz of Mauritania, Amadou Toumani Toure of Mali and Denis Sassou Nguesso of the Republic of Congo, along with Uganda's Foreign Minister Henry Oryem Okello, were travelling on separate planes.
Earlier, a statement from the South African presidency said: 'The [African Union] committee has been granted permission by NATO to enter Libya and to meet in Tripoli with..Col Qathafi. The AU delegation will also meet with the Interim Transitional National Council in Benghazi on 10 and 11 April.'
The five-strong panel was approved by the European Union to mediate in Libya.
Panel spokesman Abdel Aziz said: 'The main objective of the panel is to put an end to the war and to find an adequate solution to the crisis.'
The mission will face a difficult task as the rebels have refused to discuss a ceasefire without the removal of Col Gaddafi and his family.
The BBC's Jon Leyne in Benghazi also says that the AU team's plan for the two sides to work together in a transition to democracy looks to be a non-starter.
He says it appears that neither side is ready to make the compromises necessary for a ceasefire.
Fierce fighting is raging for a second day in Ajdabiya. Heavy gunfire and loud explosions were heard in the town on Sunday, with reports of intense shelling of the town from the west, from where pro-Gaddafi forces are attacking.
Ajdabiya is the last town before the rebels' main city of Benghazi -BBC