Fierce street fighting erupted in Muammar Gaddafi's sole remaining bastion of Sirte on Tuesday, as US Secretary of State Hillary Clinton paid a surprise visit to Tripoli.

National Transitional Council (NTC) fighters suffered at least 11 dead and 95 wounded, as Sirte's streets reverberated with the sound of heavy gunfire, rockets and mortars, medics at the two field hospitals on either side of Sirte told AFP.

Fighters were running in their hundreds through the streets of the last two neighbourhoods still in the hands of the loyalists, the Dollar and Number Two, an AFP correspondent reported.

Among those killed was Mustafa bin Dardef, a popular field commander with the Zintan Brigade, who was hit by a mortar round. A businessman in Benghazi before he joined the uprising, he leaves a son and four daughters.

"They are shooting at us from everywhere, with snipers, mortars and RPGs (rocket-propelled grenades)," said one fighter, Tahar Burzeza. "It is brutal inside. We are being shot from everywhere."

American filmmaker Matthew van Dyke, who took up arms with the rebels after he was released in August from six months in Gaddafi's notorious Abu Salim prison, was in the thick of Tuesday's fighting on the eastern side of Sirte.

"I think a lot of fighters are also getting hit by what could be friendly fire," because fighters from Misrata were also shooting from the western side, he said.

Another fighter, Abdel Basit Hadia, said: "The target is to end the fight today or tomorrow. We are encircling them" in Number Two.

In the desert oasis of Bani Walid, the red, black and green flag of the new government was raised after the only other remaining holdout was liberated on Monday.

NATO said it was not yet ready to end to its mission over Libya despite the advances made by NTC forces.

"It is premature to set a timetable now," NATO spokeswoman Carmen Romero said ahead of a regular meeting of alliance ambassadors on the Libya operation on Wednesday.

"We are very close to the end, but there are still threats to the civilian population."

Clinton echoed the comments on her visit to Tripoli, the first by a US cabinet official since Gaddafi's overthrow.

"We recognise the bloody fighting continues," she told NTC chairman Mustafa Abdel Jalil and interim premier Mahmud Jibril.

"NATO and the international coalition ... will continue to protect Libyan civilians until the threat from Gaddafi and those who hang to the past is ended."

Clinton told students at Tripoli University that she hoped the fugitive strongman would soon be captured or killed.

"The most important thing to do right now is to make sure that Gaddafi and his regime are finally prevented from disrupting the new Libya," she said.

"We hope he can be captured or killed soon, so you don't have to fear him any longer."

She said once that had been accomplished, she hoped Libyans would turn the page.

"Then you have to move forward," she said, urging the students not to waste time "trying to settle scores of the past".

A senior US State Department official accompanying Clinton acknowledged the strongman would remain a distraction from the construction of a new Libya as long as his whereabouts remained a mystery.

"None of us know where Gaddafi is," the official told the travelling press, speaking on condition of anonymity.

"But he has people -- henchmen, loyalists, sons -- here and there, who still have circles around them," he added.

"I don't think there's any coordination going on between them. I think you are having pockets of people who are trying to stop the flow of history ahead.

"He still is providing a lethal nuisance factor that is a distraction for many Libyans. But the people of Libya by large measure are already plotting .... the future of Libya without Gaddafi."