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The BBC's Wyre Davies reports from Gaddafi's compound which has been ransacked by rebels
Libyan rebels and forces loyal to Col Muammar Gaddafi have fought running battles in Tripoli, a day after the fugitive leader's compound was overrun.
There have been fierce firefights in Bab al-Aziziya, as well as in several southern and central areas of the city.
However, foreign journalists have been allowed to leave a hotel where they have been confined for several days.
Col Gaddafi's whereabouts are unknown, but overnight he vowed in a speech to fight until victory or martyrdom.
A pro-regime television channel, al-Uruba, broadcast an audio statement in which he said his decision to leave his Bab al-Aziziya compound was a "tactical" move.
He urged Libyans to cleanse the streets of "traitors, infidels and rats", and said he had "been out a bit in Tripoli discreetly, without being seen".
"It did not feel like Tripoli had fallen or someone had marched into it."
Muammar Gaddafi may have lost political control of the country he ruled with an iron grip for more than 40 years, but his loyal troops are refusing to go quietly.
As I went inside his former compound in the heart of Tripoli this morning, I saw rebel fighters being pushed back as a fierce fire-fight ensued in the inner circle of Bab al-Aziziya. These men, many of whom will have protected their leader for many years and are well-armed and professional soldiers, will almost certainly fight to the death. All day long, gunfire and artillery fire has hit the compound with those inside firing out.
Few of the rebel fighters are yet ready to talk about whatever political future faces Libya post-Gaddafi. Their immediate goal is to capture or kill a man who has said he will fight until the bitter end.
Later, the rebel National Transitional Council (NTC) offered an amnesty to anyone within Col Gaddafi's "inner circle" who captured or killed him. It said a Libyan businessman was also offering a $1.67m (£1m) reward.
Correspondents say it is an obvious attempt to sow divisions among Gaddafi loyalists.
Libyan Foreign Minister Abdul Ati al-Obeidi told the UK's Channel 4 News that it appeared Col Gaddafi had exhausted all his options, including fleeing abroad, and that his rule "was over".
Rebel commanders had earlier said it was vital to capture Col Gaddafi to eliminate any chance he could strike back.
They insisted it was only a matter of time before he was found, but conceded they had no indication of where he might have taken refuge.
One rebel official, who gave his name as Abdul Rahman, told the Reuters news agency that it was thought that Col Gaddafi was still in Tripoli, possibly in the al-Hadhba al-Khadra area, where there was fighting.
He is also believed to retain a strong following in two other cities - Sirte, his hometown 450km (280 miles) to the east of the capital, and Sabha, 650km to the south in the desert.
Analysts say Sabha has a significant military and air force base and, if Col Gaddafi and his family can reach it, it would provide them the option of easy desert escape routes into Niger or Chad.
A rebel spokesman told the BBC that negotiations were going on with local leaders in Sabha and Sirte seeking a peaceful end to the conflict.
'Fight to the death'
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The BBC's Matthew Price on life in Rixos hotel: "Gunmen still believed the city could be won"
Despite thousands of rebel fighters overrunning Col Gaddafi's Bab al-Aziziya compound in Tripoli on Tuesday evening, they were still meeting fierce resistance from well-armed loyalists on Wednesday.
The BBC's Wyre Davies says the rebels are using artillery to try to flush out gunmen entrenched in the centre of the compound.
Many of the loyalists are members of the fugitive leader's tribe or professional soldiers, and are prepared to fight to the death, our correspondent adds.
"There are snipers above and around the perimeter of Bab al-Aziziya; there are dozens of them but we don't know where they are," rebel commander Nouri Mohammed told the AFP news agency.
There was also heavy gunfire in the area around the capital's Rixos Hotel, where about 30 foreign journalists - including a five-person team from the BBC - were confined for several days by Gaddafi loyalists armed with automatic weapons. They have all now been allowed to leave.
"When we got driven out, we discovered we had been inside a 200 sq m piece of Tripoli, where two gunmen believed that they were fighting still on behalf of Col Gaddafi, and that the battle was still going on for Tripoli even though the whole world had seen the city had fallen," said the BBC's Matthew Price, who was among those trapped.
"It was firmly their belief that if we went outside of the hotel, the rebels would capture us, kill us or rape the women."
There were also reports that that pro-Gaddafi forces had hidden on the road to the international airport, and that the fighting had spread to the areas of Abu Salim and al-Zuwara.
Witnesses say armed residents in Tripoli are continuing to man makeshift checkpoints with the help of rebel fighters.
Law and order does not appear to have broken down and celebrations have been continuing in Green Square.
The National Transitional Council estimates that about 400 people have been killed and thousands injured in the battle for Tripoli since Sunday.
The International Red Cross says the fighting in Tripoli has left many civilians injured. A spokesman said doctors were finding it difficult to reach hospitals in and around the capital because of continuing battles.
Funding appeal
Earlier, an NTC spokesman told the BBC it had started the process of moving its headquarters to Tripoli from its stronghold of Benghazi.
He said several council members were already in the capital and others were on their way.
But the BBC's Jon Leyne in Benghazi said that with Gaddafi loyalists still fighting back, the NTC seems hesitant about a full move.
The rebels also confirmed on Wednesday that their swift advance on Tripoli was part of a long-planned operation - Mermaid Dawn - that was co-ordinated with Nato. Groups of rebels were trained in Benghazi then sent undercover to the capital, to wait for the signal to fight.
NTC representatives have also been preparing for high-level talks in Qatar with envoys of the US, UK, France, Turkey and the UAE to discuss how to move ahead in a post-Gaddafi Libya.
The head of the NTC's cabinet, Mahmoud Jibril, said it was seeking $2.5bn (£1.5bn) in immediate aid.
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Rebel spokesman Guma el-Gamaty explains the amnesty for anyone who captures or kills Col Gaddafi
Its immediate priority is to pay employees' salaries and cover humanitarian costs but, in the longer term, money will be needed to repair Libya's oil infrastructure.
Mr Jibril estimates that Libya has some $160-170bn in frozen assets. The US has said it will try to release up to $1.5bn, while British and French diplomats are working with their allies to draft a resolution that would free funds blocked by UN Security Council sanctions.
Mr Jibril will later meet French President Nicolas Sarkozy in Paris. A statement from the Elysee Palace said the talks would focus on the international community's actions to support a free and democratic Libya.
The uprising against Col Gaddafi's 41-year rule began in February. The rebels held the east of the country and pockets of the west, before making their push towards the capital at the weekend.
Nato air strikes have been targeting Col Gaddafi's forces, acting on a UN mandate to protect civilians. Critics accuse it of siding with the rebels.