Earlier, crowds in Benghazi cheered UK Prime Minister David Cameron and French President Nicolas Sarkozy.
They are the first foreign leaders to visit Libya since Col Gaddafi fell.
A spokesman for the National Transitional Council (NTC) told the BBC that NTC fighters have breached lines of defence on the south and west of Sirte.
The fighters - made up of battalions from Misrata, 200km (120 miles) to the west - are about 8-10km from the city centre, the spokesman said.
They have been facing fierce resistance and have been forced to withdraw a couple of kilometres in order to treat casualties, he added.
Ali Gliwan of the NTC told the Associated Press news agency the fighters had advanced into Sirte city centre, where they clashed with snipers and an elite unit of pro-Gaddafi troops.
Four NTC fighters had been killed and seven wounded, he told AP.
Col Gaddafi's spokesman, Moussa Ibrahim, told a Syrian TV channel that "thousands of volunteers" were ready to "liberate Libya" from the NTC.
"There are thousands upon thousands of young volunteers who are ready on the various fronts," he said in a phone call to the pro-Gaddafi al-Rai channel.
He went on: "We are in fact strong. We have the capabilities, the means and plans to liberate the whole of Libya."
Rapturous reception Mr Cameron and Mr Sarkozy arrived in Tripoli on Thursday morning where they held talks with Libya's interim leader, NTC chairman Mustafa Abdul Jalil.
They pledged support for the NTC and announced a series of measures, including the unfreezing of billions in Libyan assets and funding for landmine clearance.
They then under heavy security travelled to Benghazi, the NTC's eastern stronghold and the seat of Libya's revolution.
There, thousands of people filled central Liberty Square, cheering so loudly that the leaders struggled to make themselves heard.
"It is great to be in free Libya," Mr Cameron told the crowd. "Col Gaddafi said he would hunt you down like rats, but you showed the courage of lions."
Mr Sarkozy plunged into the crowd, reaching across his bodyguards to shake the hands of waiting Libyans, many of them waving French flags.
'Brave positions' During his one-day visit, Mr Cameron praised the NTC for the way it has established control over the country, but warned that the "hardest part" was still to come.
"The message, I think, to Gaddafi and all those holding arms on his behalf is: it is over. Give up. The mercenaries should go home," Mr Cameron told a news conference in Tripoli.
Mr Abdul Jalil thanked them for taking "brave positions" during the Libyan uprising.
"They showed us political, economic and military support which helped the rebels establish a state, and we thank France and the UK for that," he said.
Mr Sarkozy urged Libyans to avoid "vengeance and retaliation", calling on them to preserve unity and seek reconciliation.
Missing gold On Friday, the NTC is to send a delegation to neighbouring Niger in an effort to recover gold and cash believed to have been taken out of Libya by fleeing Gaddafi loyalists.
Mr Sarkozy and French Foreign Minister Alain Juppe will also meet Niger's leadership on Friday.
"Impunity is over," Mr Sarkozy said.
At least 36 members of the fugitive leader's inner circle, including relatives and generals, have fled to neighbouring Algeria and Niger since Tripoli fell to NTC forces last month.
Mr Abdul Jalil said Libya would also ask for the handover of individuals wanted by the International Criminal Court (ICC).
The ICC has indicted Col Gaddafi, his son Saif al-Islam and his intelligence chief for crimes against humanity.