A reward of £1m is being offered for whoever finds Colonel Muammar Gaddafi, dead or alive, the head of the Transitional National Council (NTC) has said.
Pro-Gaddafi forces have attacked several locations in central Tripoli, according to rebel sources, including the colonel's former compound.
Col Gaddafi is believed to be hiding somewhere in the city and Mustafa Abdel-Jalil said: "The NTC supports the initiative of businessmen who are offering two million dinars (£1m) for the capture of Muammar Gaddafi, dead or alive."
Mr Jalil said the NTC was offering an amnesty to any of Col Gaddafi's entourage who kill or capture him.
Sky's security editor Sam Kiley, in Libya, said it is two businessmen based in Benghazi who are offering the money.
Fighting is still taking place in large parts of Tripoli with reports of an escalation in sniper fire resulting in deaths and casualties.
Sky's Stuart Ramsay, in Tripoli, said there had also been reports of 500 non-Libyan mercenaries being arrested near the airport, which is held by the rebels.
Earlier, journalists who were trapped inside the Rixos hotel in the capital for the past six days were allowed to leave.
And the US has asked the UN Security Council to unfreeze \$1.5bn of Libyan assets for humanitarian needs but diplomats said South Africa had objected.
A vote is likely to be held on Thursday.
Officials from the Libya contact group have met in Doha to discuss providing \$2.5bn in urgently required funds for the rebels' governing council and unfreezing Libyan assets globally.
The meeting, attended by representatives of the US, France, Britain, Italy, Germany and Turkey, was held at the request of the NTC.
Speaking in a press conference with NTC head Mahmoud Jibril earlier, France's President Nicolas Sarkozy praised the "courage and tenacity" of the Libyans and pledged his support for the council.
Mr Sarkozy said France was ready to continue military operations under the UN resolution framework for as long as needed.
An international conference, led by Mr Sarkozy and British Prime Minister David Cameron, will be held in Paris on September 1 with the NTC and countries that are "friends of Libya" invited.
On Wednesday morning, a rebel spokesman said: "There were bombardments on Bab al Aziziyah (compound), Al Mansoura area.
"Most of this bombardment was carried out by the regime's cells positioned in the Abu Salim area."
As the dictator's forces continue to hit back, members of the rebels' transitional government are preparing for a move to Tripoli, where they intend to establish an interim administration.
The counter-attack comes as Col Gaddafi called for the city's residents to "cleanse" the capital of insurgents in an audio broadcast on Syrian television.
He told Al-Rai TV: "All Libyans must be present in Tripoli, young men, tribal men and women must sweep through Tripoli and comb it for traitors.
"I have been out a bit in Tripoli discreetly, without being seen by people, and...I did not feel that Tripoli was in danger," he said.
A woman, claiming to be Col Gaddafi's daughter Aisha, has told the al Orouba TV channel Libyans must unite against Nato and foreign interference.
"I tell the Libyan people to stand hand-in-hand against Nato," she told the station by telephone. "I tell the Libyan people not to fear the armed forces. The leader is in the right."
But Col Gaddafi's support network appears to be collapsing around him.
Al Arabiya TV has reported that Libya's deputy chief of intelligence has quit and declared allegiance to the opposition force.
Rebels swept into Col Gaddafi's compound on Tuesday, seizing weapons and destroying symbols of the longstanding dictatorship.
The jubilant fighters celebrated their rapid advance and erected their flag above the base.
One man found Col Gaddafi's gold-trimmed hat in his bedroom inside the compound and was wearing it as he told Sky News he planned to give it to his father.
There is widespread speculation that Col Gaddafi may have used a secret network of tunnels to escape and the US believes he remains in the country.
He has reportedly told an Arabic television station that his withdrawal was a tactic and promised death or victory against rebels.
Abdel Hakim Belhadj, a rebel commander, said he did not know where the dictator or his sons were, saying: "They ran like rats."
Col Gaddafi's remaining forces are said to be heading for his home town of Sirte, raising fears of a bloody final showdown with the rebels.
Opposition leaders said 400 people have been killed and 2,000 wounded during three days of fighting in Tripoli.
Celebrations took place across the country as the rebels' success became clear and thousands gathered in Tripoli's Green Square - now renamed Martyrs' Square.
But reports of hostile fire around the city centre overnight suggested the six-month popular insurgency had not completely triumphed yet.
Mustafa Abdel-Jalil, who was until February a loyal minister of Col Gaddafi, warned: "It is too early to say that the battle of Tripoli is over.
"That won't happen until Gaddafi and his sons are captured."
Col Gaddafi has vowed death or victory in the fight against "aggression", telling Al-Orouba TV that his Tripoli headquarters had been levelled after 64 Nato airstrikes.
Col Gaddafi's main spokesman, Moussa Ibrahim, told the same channel the regime could resist rebels for "months or even years" and would be "back to take Tripoli back".
He vowed Libya would be turned into "volcanoes, lava and fire".