The ceasefire offer came as UN envoy Abdelilah al-Katib visited Libya
A Libyan government spokesman has termed the conditions set by the opposition for a ceasefire "mad", and asserted that troops loyal to Muammar Gaddafi, the Libyan leader, will remain stationed where they are.
"They are asking us to withdraw from our own cities. .... If this is not mad then I don't know what this is. We will not leave our cities," Mussa Ibrahim, the government spokesman, said on Friday.
Fighting raged on Friday near the key oil town of Brega, in the country's east, and the towns of Misurata and Az Zintan in the west.
Earlier, the opposition had said it would agree to a ceasefire as long as Gaddafi pulled his military out of opposition-held cities and allowed peaceful protests against his government.
Mustafa Abdul-Jalil, head of the opposition's interim governing council based in Benghazi, spoke during a joint press conference on Friday with Abdelilah Al-Khatib, the UN envoy. Al-Khatib is visiting the rebels' de facto stronghold of Benghazi in hopes of reaching a political solution to the crisis embroiling the North African nation.
Abdul-Jalil said the rebels' condition for a ceasefire is "that the Gaddafi brigades and forces withdraw from inside and outside Libyan cities to give freedom to the Libyan people to choose and the world will see that they will choose freedom".
The UN resolution that authorised international air strikes against Libya called for Gaddafi and the rebels to end hostilities. Gaddafi announced a ceasefire immediately but has shown no sign of heeding it. His forces continue to attack rebels in the east, where the opposition is strongest, and have besieged the only major rebel-held city in the west, Misurata.
Abdul-Jalil said the regime must withdraw its forces and lift all sieges. He stressed the ultimate goal was still to oust Gaddafi.
"Our aim is to liberate and have sovereignty over all of Libya with its capital in Tripoli," he said.
Al Jazeera's Laurence Lee, reporting from Benghazi, played down the significance of the statements, noting that this is not the first time the rebels have said they are open to negotiation.
"You have to remember that Mr Abdel Jalil was saying it in the presence of the United Nations special envoy to Libya, and the UN is calling repeatedly for a ceasefire, and so he had to acknowledge that to some degree," Lee said.
"But the other thing you have to remember that he said, was that if there is no ceasefire then the rebels will press on to try to liberate all the Western towns."
Despite the continued bravado, the protracted stalemate and shortage of arms is clearly causing unease in the opposition stronghold, he said.
"As time goes by, the military solution to this looks far less likely, and I think the political solution, if not inevitable, looks far more likely," he reported.
Forces loyal to Libya's leader of nearly 42 years spent much of this week pushing the rebels back about 160km along the coast. Attempting to regroup, the rebels hit back with mortars on Friday - weapons they previously appeared to have lacked. The previous night, they drove in a convoy with at least eight rocket launchers - more artillery than usual.
The rebels also appeared to have more communication equipment such as radios and satellite phones, and were working in more organised units, in which military defectors were each leading six or seven volunteers.
On Friday, they appointed Abdel Fatah Yunis, the former interior minister who resigned to join the opposition, as the commander of the opposition military forces combatting pro-Gaddafi brigades.
The rebels' losses this week, and others before airstrikes began March 19, underlined the reality that their equipment, training and organisation were far inferior to those of Gaddafi's forces. The recent changes appear to be an attempt to correct, or at least ease, the imbalance.
Residents of Misurata, meanwhile, said they came under heavy bombardment throughout the day from pro-Gaddafi forces.
"They used tanks, rocket-propelled grenades, mortar rounds and other projectiles to hit the city today. It was a random and very intense bombardment," Sami, a rebel spokesman, told Reuters by telephone. "We no longer recognise the place. The destruction cannot be described."
Opposition fighters were locked in combat with pro-Gaddafi forces near Brega on Friday [Reuters]
Opposition fighters say government forces are targetting both the city's port and residential areas.
Heavy fighting also took place near the key oil port of Brega, where doctors told the AFP news agency that 11 people had been killed.
Meanwhile, in the village of Argkuk, near Ajdabiya, Al Jazeera's Sue Turton reported that what appeared to be a NATO-led coalition airstrike on a pro-Gaddafi vehicle killed seven civilians and injured 25 others when ammunition in the vehicle exploded.
Ibrahim, the government's spokesman, termed the strike a "crime against humanity".
It was unclear where the frontline was Friday. Rebels were holding journalists back at the western gate of Ajdabiya, far from the fighting. On Thursday the opposition had moved into Brega before Gaddafi's forces pushed them out.
A Libyan opposition official, meanwhile, said rebels would be able to buy more arms thanks to an oil deal they reached with the Arab nation of Qatar.
Ali Tarhouni, who handles finances for the opposition's National Transitional Council, said Qatar has agreed to market oil currently in storage in rebel-controlled areas of southeastern Libya.
Tarhouni said one sticking point is how to truck the oil out of the country. The money from oil sales will be put into an account which the opposition will use to pay for weapons, food, medicine, fuel and other needs.
Defections take toll
Gaddafi's greatest losses this week were not military but political. Two members of his inner circle, including his foreign minister, abandoned him this week, setting off speculation about other officials who may be next.
The defections could sway people who have stuck with Gaddafi despite the uprising that began February 15 and the international airstrikes aimed at keeping the Libyan leader from attacking his own people.
Gaddafi struck a defiant stance in a statement Thursday, accusing the leaders of the countries attacking his forces of being "affected by power madness".
Al Jazeera's Hoda Abdel-Hamid reports from the
opposition's front lines near Brega
"The solution for this problem is that they resign immediately and their peoples find alternatives to them," he said.
Yet Gaddafi's message was undercut by its delivery - a scroll across the bottom of state TV as he remained out of sight.
Meanwhile, nations behind the campaign of international airstrikes that have hobbled Libya's military hailed the resignation and flight to the UK of Gaddafi's foreign minister, Moussa Koussa, as a sign of weakness in Gaddafi's reign.
Koussa has been privy to all the inner workings of the regime, so his departure could open the door for some hard intelligence, though Britain refused to offer him immunity from prosecution.
Ali Abdessalam Treki, a former foreign minister and UN General Assembly president, announced his departure on several opposition websites the next day, saying "It is our nation's right to live in freedom and democracy and enjoy a good life".
Treki's defection comes after Al Jazeera uncovered what was supposed to be a secret visit to Tunis in mid-March.
The rebels say they have taken heart from the departures in Gaddafi's inner circle.
"We believe that the regime is crumbling from within," opposition spokesman Mustafa Gheriani said in Benghazi, the rebels' de facto capital.