Rebels have been engaged in fierce firefights with government forces in mountain plains about 80km (50 miles) south-west of Tripoli.
A BBC correspondent who was with the rebels was told by a volunteer medic two of them had died in the battle.
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.
'Consolidating gains'
The BBC's Mark Doyle, who is in the village of Bir Ayad, a strategic point on the road to the capital, Tripoli, says Sunday's fighting began when government forces tried to cut off the rebels by attacking from behind.
The fighting was continuing in the distance where the boom of artillery, the rattle of automatic gunfire and the occasional rumble of Nato jets could be heard, he says.
The rebels came down into the plains from the Nafusa mountains in early June, adds our correspondent, and say they are approaching the gates of Tripoli. But they have met strong resistance from Col Gaddafi's forces.
He says that although it is a shifting front line, the rebels appear to be gradually consolidating their position in the western mountains.
The front line is now thought to have moved just north of Bir Ayad to near the town of Bir al-Ghanam.
An AFP correspondent nearby heard heavy fire from rockets and machine-guns.
Guma el-Gamaty, a spokesman for the rebels' National Transitional Council, told AP news agency Bir al-Ghanam was important as it was barely 30km south of Zawiya, a western gateway to Tripoli.
Opposition fighters seized Zawiya in March before government troops drove the rebels out of the oil-refinery city. Fighting again broke out there this month.
The minister of defence for Libya's rebels, Jalal al-Dgheli, told the BBC that because their weapons were so limited, most of them were focused on the push from the western mountains towards Tripoli.
But in the near future there could be an advance from the east near Brega towards Tripoli, he told the BBC's Bridget Kendall in the rebel stronghold of Benghazi.
He added: "What we're learning from defectors is that Gaddafi's supporters are getting fewer, people who are close to him are abandoning him, and his inner circle is getting smaller by the day."
'Election proposal'
The Libyan government on Sunday meanwhile reportedly renewed its offer for a vote on whether Col Gaddafi should stay in power.
Gaddafi spokesman Moussa Ibrahim was quoted as telling reporters in Tripoli that the government was proposing a period of national dialogue and an election overseen by the UN and African Union.
A Libyan woman fires at a graduation ceremony after a weapons training course in Tripoli "If the Libyan people decide Gaddafi should leave he will leave," Mr Ibrahim was quoted by Reuters news agency as saying. "If the people decide he should stay he will stay."
But he said Col Gaddafi - who has run the oil-producing country since a military coup in 1969 - would not go into exile.
The idea of holding an election was first raised earlier this month by one of Col Gaddafi's sons, Saif al-Islam.
Since then Italy has called for a political settlement to the conflict, following a Nato strike in Tripoli on 19 June that killed several civilians.
As African leaders met in Pretoria on Sunday, South African President Jacob Zuma, who met Col Gaddafi in Tripoli last month, repeated his criticism of Nato air strikes.
"Civilian lives have been lost due to these bombs, and civilian infrastructure has suffered untold damage," Mr Zuma said.
Meanwhile, more than 100 Libyans arrived in Tripoli by ship from the eastern rebel stronghold of Benghazi early on Sunday.
The ferry was operated by the Red Cross, which transported about 300 people in the opposite direction on Friday.
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