Rebels have been engaged in fierce firefights with government forces about 80km (50 miles) south-west of Tripoli and close to their frontline.
A BBC correspondent who was with the rebels said two of them had died in the battle, according to a volunteer medic.
The rebels said government forces suffered far greater casualties, although that cannot be confirmed.
Meanwhile, Col Muammar Gaddafi has agreed to stay out of talks on ending the conflict, African leaders said.
In a communique after talks on Sunday in South Africa, the African Union panel on Libya said it “welcomes Colonel Gaddafi’s acceptance of not being part of the negotiations process”. The statement did not elaborate.
The frontline is now thought to have moved just north of Bir Ayad to near the town of Bir al-Ghanam.