A son of Muammar Gaddafi, previously reported captured, made a surprise appearance with jubilant supporters in Tripoli overnight, urging loyalists to fight off rebels who say they control most of the Libyan capital.

Saif al-Islam, seen as his father's chosen successor, visited the Tripoli hotel where foreign journalists are staying to declare that the government was defeating its opponents.

He took journalists to his father's fortified Bab al-Aziziya bastion in central Tripoli early on Tuesday. Saif smiled, waved, shook hands with supporters and flashed victory signs.

"We broke the back of the rebels. It was a trap. We gave them a hard time, so we are winning," he said.

"Take up arms today," Saif told cheering supporters waiting to be given weapons. "Inshallah (God willing), we will attack the rats today."

Saif's arrest had been reported both by rebels and the International Criminal Court (ICC) in The Hague, and his reappearance raised questions about the rebels' credibility.

Saif said Tripoli was in government hands and that he did not care about the arrest warrant issued by the ICC to put him and his father on trial for crimes against humanity.

Asked if his father, who has not been seen in public for weeks, was safe and well in Tripoli, Saif said: "Of course."

Saif's reappearance mystified rebels.

"We're trying to figure out how he escaped," said one rebel, Muftah Ahmad Uthman. "You know the capital was captured really quickly. Many of the men in uniform are volunteers, and some of them make mistakes."

World leaders urged Gaddafi, 69, to surrender to prevent more bloodshed and appealed for an orderly transition of power, as the six-month-old battle for control of the oil-producing North African nation appeared to enter its final stages.

FIREFIGHTS

Rebels swept into Tripoli two days ago in tandem with an uprising within the city. Reuters reporters saw firefights and clashes with heavy weapons, including anti-aircraft guns, as rebels tried to flush out snipers and pockets of resistance.

Hundreds seem to have been killed or wounded since Saturday. But Gaddafi tanks and sharpshooters appeared to hold only small areas, mainly around the Bab al-Aziziyah compound.

Civilians, who had mobbed the streets on Sunday to cheer the end of dictatorship, stayed indoors as machinegun fire and explosions punctuated some of the heaviest fighting of the Arab Spring uprisings that have been reshaping the Middle East.

U.S. President Barack Obama, saying the conflict was not over yet, cautioned rebels against exacting revenge for Gaddafi's brutal rule. "True justice will not come from reprisals and violence," he said.

The president also made plain that the United States would oppose any group within the loose coalition of rebels from imposing its power over other parts of Libyan society.

"Above all we will call for an inclusive transition that leads to a democratic Libya," Obama said.

In an audio broadcast on Sunday before state TV went off the air, Gaddafi said he would stay in Tripoli "until the end". There has been speculation, however, he might seek refuge in his home region around Sirte, or abroad.

In a sign Gaddafi allies were still determined to fight, NATO said government forces fired three Scud-type missiles from the area of Sirte towards the rebel-held city of Misrata.

Rebels clashed with an army convoy coming from Sirte, killing dozens of Gaddafi's troops on Tuesday, Al Arabiya TV reported. It did not say where the clash took place. NATO bombed Sirte heavily just before rebels moved into Tripoli.

Bab al-Aziziya, a huge complex where some believe Gaddafi might be hiding, was the focal point of fighting in Tripoli.

"I don't imagine the Bab al-Aziziya compound will fall easily and I imagine there will be a fierce fight," Abdel Hafiz Ghoga, spokesman for the rebel National Transitional Council, said in an interview aired by Al-Jazeera.

The Arab network, quoting its correspondent, said violent clashes were also reported near the oil town of Brega.

Rebels had initially said they held three of Gaddafi's sons, including Saif al-Islam. Al-Jazeera TV said that one of them, Mohammed, had escaped, adding that the body of another son, military commander Khamis, might have been found along with that of powerful intelligence chief Abdullah al-Senussi.

FEARS OF REPRISAL, REVENGE

Western powers are concerned that tribal, ethnic and political divisions among the diverse armed groups opposed to Gaddafi could lead to the kind of blood-letting seen in Iraq after the overthrow of Saddam Hussein.

In a move that could ease tensions, a rebel official in the eastern city of Benghazi said, however, that efforts were under way to make contact with authorities hitherto loyal to Gaddafi.

Foreign governments which had hesitated to take sides, among them Gaddafi's Arab neighbours, Russia and China also made clear his four decades of absolute power were over.

A U.S. State Department spokeswoman said Libyans who said they represented Gaddafi were making "more desperate" efforts to negotiate with the United States in the last 24 to 48 hours.

Washington did not take any of them seriously because they did not indicate Gaddafi's willingness to step down, she added.

French President Nicolas Sarkozy, who took an early gamble on the rebels and may now reap diplomatic benefits, called on the Gaddafi loyalists "to turn their back on the criminal and cynical blindness of their leader by immediately ceasing fire".

Late on Monday, Sarkozy spoke to Britain's David Cameron by telephone about Libya, and they agreed to "pursue efforts in supporting the legitimate Libyan authorities as long as Colonel Gaddafi refuses to surrender arms," a French statement read. Paris has offered to host a summit on Libya soon.

Cameron also spoke to Obama on Monday night.

OIL PRODUCTION

Western leaders, wary of a possible Iraq-style insurgency by rearguard Gaddafi loyalists, reiterated their refusal to commit military forces to peacekeeping in Libya.

Britain's International Development Secretary Andrew Mitchell told the BBC his country saw no circumstances in which British troops would be deployed on the ground in Libya.

But some governments have had civilian advisers in Benghazi for months, and recent swift rebel advances revived questions about the shadowy role of foreign special forces on the ground.

First signs emerged of moves to begin restoring oil output that has been the basis of the economy and a source of hope for Libya's 6 million, mostly poor, people. Staff from Italy's Eni arrived to look into restarting facilities, said Foreign Minister Franco Frattini.

He said Italy expects contracts held by Italian companies in Libya to be respected by any new post-Gaddafi government.

Italy's interests in its former colony stretch from oilfields to huge contracts in defence and construction.

"They've agreed to honour all contracts, including those with Italian companies, undertaken by Libya," Frattini told Italian radio, referring to the Benghazi-based rebel council. "Italy's contracts are with Libya, not with Gaddafi."

Italy is a big customer for Libyan energy. But it will face stiff competition from others seeking a share of Libya's wealth -- a competition some fear could test the ability of untried rebel leaders to hold the country together.

Once Gaddafi's closest European ally, Rome has been courting the rebels since April.

Frattini said the situation in Tripoli remained uncertain.

"We certainly have confirmation of a rising presence of the opposition, the so-called rebels, in various neighbourhoods of Tripoli, including the international airport area.

"This is a time of great confusion, also because there are clashes in some parts of the city; mainly around the fortified compound that has been the refuge -- and presumably still is -- of the dictator Gaddafi," Frattini said, adding that the only people on Gaddafi's side were snipers and mercenaries.