A National Transitional Council spokesman said the fighters had breached Sirte's defences but were meeting heavy resistance.
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) said 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 said.
Col Gaddafi's spokesman, Moussa Ibrahim, told a Syrian TV channel that "thousands of volunteers" were ready to "liberate Libya" from the NTC.
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