Col Gaddafi's whereabouts are unknown, though rebels have said they think he is still in or around Tripoli.
Rebels fighters have fought running battles in the capital, where pockets of pro-Gaddafi resistance remain.
The fugitive leader has vowed in an audio message to fight until victory or martyrdom.
His sprawling Bab al-Aziziya compound was overrun on Tuesday, though firefights within the complex have continued.
Col Gaddafi's forces are still firmly in control of his birthplace - the strategic coastal city of Sirte - as well as several key bases in southern Libya.'Huge incentive'
The head of the National Transitional Council (NTC), Mustafa Abdel Jalil, announced the amnesty offer from the eastern city of Benghazi.
"Gaddafi's forces and his accomplices will not stop resisting until Gaddafi is caught or killed," he said.Continue reading the main story
Libyan rebels as well as Nato officials will be hoping that the hunt for Col Muammar Gaddafi does not turn into a protracted affair. ”End Quote Gordon Corera Security correspondent, BBC News He added that the NTC supported an offer by a group of businessmen to pay $1.7m for Col Gaddafi, "dead or alive".
Rebel spokesman Guma el-Gamaty told the BBC that those around Col Gaddafi were "heavily implicated with him in crimes against humanity and crimes against the Libyan people".
"Now there is a huge psychological incentive for them. If they don't want to go down with him and save their skin, they will be immune from prosecution if they hand him over or kill him," he said.
The rebel leadership have also offered Col Gaddafi safe passage out of the country, if he renounces his leadership.
Mr Gamaty said such a possibility was remote.
"I think [Col Gaddafi] would rather die or be captured than do that," he said.'Tactical move'
Despite thousands of rebel fighters overrunning Col Gaddafi's Bab al-Aziziya compound in Tripoli on Tuesday, they were still meeting fierce resistance from well-armed loyalists a day later.Rebel spokesman Guma el-Gamaty explains the amnesty for anyone who captures or kills Col Gaddafi
Col Gaddafi 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.
A rebel spokesman told the BBC that negotiations were going on with local leaders in both locations seeking a peaceful end to the conflict.
The NTC estimates that about 400 people have been killed and thousands injured in the battle for Tripoli since Sunday.
Earlier, Col Gaddafi said in an audio message that his decision to leave his Bab al-Aziziya compound was a "tactical" move.
He said he had "been out a bit in Tripoli discreetly, without being seen".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".
And the deputy head of Libyan intelligence, Gen Khalifa Mohammed Ali, declared his allegiance to the rebels in an interview with Saudi-owned al-Arabiya TV channel.
Meanwhile, the head of the NTC's cabinet, Mahmoud Jibril, said it was seeking $2.5bn in immediate aid.
Its immediate priority is to pay employees' salaries and cover humanitarian costs, though in the longer term, money will be needed to repair Libya's oil infrastructure, correspondents say.
Diplomats say the US will present a draft resolution at a meeting of the UN Security Council on Wednesday evening asking it to release $1.5bn of assets for humanitarian needs. A vote is expected on Thursday or Friday.
But South Africa has been stalling Washington's attempts, saying it wants to wait for guidance from the African Union, which has not recognised the rebel leadership as Libya's legitimate authority.
Meanwhile, the NTC says it has started the process of moving its headquarters from Benghazi to Tripoli, but that with Gaddafi loyalists still fighting back, a full move has been postponed until next week at the earliest.
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