Sirte, one of the last bastions of support for the deposed Libyan leader, is encircled by forces with the interim government and under bombardment from NATO warplanes.
Touhami Zayani, commander of the El-Farouk brigade on the western edge of Sirte, told Reuters an elder from Gaddafi's tribe, whom he did not identify, had contacted him on his satellite phone from inside Sirte.
"He called me and said we are looking for a safe passage for the families and for the militia to leave the city," he said.
Zayani said he had given his agreement for families from Gaddafi's tribe, who make up the majority of Sirte's population, to be allowed to leave and was still negotiating terms for armed Gaddafi loyalists to surrender.
"We didn't really get into details and we didn't talk much about how they will leave but I think the scenario will be that they have to give up their weapons," Zayani said.
Reflecting the lack of coordination that has dogged the Libyan government's efforts to establish its authority, units in the east of Sirte fought on, even as their allies in the west of Sirte ceased fire to await the outcome of truce talks.
Asked about the prospect of a truce with pro-Gaddafi fighters, Omar Al-Qatrany, an anti-Gaddafi commander on the eastern front line, said: "Those people don't want to negotiate and we don't care about them any more.
"Our main concern is to evacuate families out of Sirte and then we will bomb the city," he said.
Libya's new rulers received an important boost when exports of crude oil -- the country's only major source of revenue -- resumed for the first time in months.
There were clashes at a roundabout 2km east of the centre of Sirte, where anti-Gaddafi fighters were pinned down for a second day by intense sniper and artillery fire.
A Reuters reporter nearby said forces with the new government, the National Transitional Council (NTC), brought up reinforcements to the roundabout to try to break through, including two tanks and about a dozen trucks carrying infantry.
Snipers, though, held up the advance, forcing the attackers to take cover behind metal shipping containers.
Medical workers at a hospital in Ras Lanuf, which lies 220km east of Sirte, said they had received the bodies of six NTC fighters killed in fighting on the city's eastern front. Some 45 fighters were wounded, many from sniper fire.
While the fighting continues, humanitarian organisations have been expressing alarm at the worsening situation in Sirte.
"Our main worry is the people being displaced because of the fighting," said Jafar Vishtawi, a delegate of the International Committee of the Red Cross (ICRC), near Sirte.
Taking Sirte, 450km east of Tripoli, would bring Libya's new rulers closer to gaining control of the whole country, something still eluding them more than a month after their fighters seized the capital.
It is likely some members of Gaddafi's family are in Sirte but there is no information about the location of the former ruler himself. He is the subject of an Interpol arrest warrant.
A Syria-based television station broadcast footage on Tuesday of what it said was Gaddafi's son Saif al-Islam, dated September 20, rallying his forces at an unidentified location.
"This land is the land of your forefathers. Don't hand it over," Saif al-Islam, shouted to a crowd of followers, according to the footage broadcast by Arrai TV.
In neighhouring Algeria, the government ordered members of Gaddafi's family in exile there to stay out of politics after Gaddafi's daughter Aisha angered the NTC by telling the media her father was still fighting to hold on to power.
"It is clear that the message has been passed on to Aisha and the other members of the family that they should, from now on, respect their status as guests in Algeria and remove themselves completely from any political action," Algerian Foreign Minister Mourad Medelci was quoted as saying by the official APS news agency.
Aisha Gaddafi, her brothers Hannibal and Mohammed, their mother Safia and several other family members fled in August.
In a separate development, a Tunisian court of appeal freed Gaddafi's former Prime Minister Al-Baghdadi Ali al-Mahmoudi, who was sentenced to six months in jail last week after he was arrested near the North African country's border with Algeria.
Shortly after the ruling, a source at the Justice Ministry told Reuters that Tunisia had not received any request from the NTC to extradite al-Mahmoudi.
"Tunisia has not received any official request to extradite Mahmoudi," the source said. "And after the court's decision to free him, he is a free man." A Tunisian court last week jailed Mahmoudi for illegally entering the country.
The head of Libya's port authority said a cargo of crude oil had sailed on Sept. 25 from the port of Marsa el Hariga, bound for Italy. It was only the third cargo to leave Libya since the rebellion against Gaddafi's rule began in February.
"We are working hard to make everything run normally at the ports," Capt. Ramadan Boumadyan said in an interview. "I think everything will be back to normal in a month's time."
Foreign companies are jockeying for a share of oil contracts and the billions of dollars in reconstruction contracts the new Libyan government is expected to hand out once revenue from oil sales starts flowing in.
Firms from Britain and France, which led the NATO bombing campaign against Gaddafi's forces, are in the forefront of the race for business.
"They (the Libyans) are not naïve, they expect it to be profitable to us, but they're not going to do us any favours. It will be competitive," Stephen Green, Britain's trade and investment minister, told a meeting of British executives in London.
The biggest risk to Libya's stability now is a power vacuum. The NTC exercises only tenuous control while real power lies in the hands of armed militias that ousted Gaddafi.
NTC officials on Tuesday asked fighters who flooded into Tripoli from other regions to leave, warning their presence could destabilise the country.
