"Our forces entered the last areas held by Daesh in Sirte: district number one and district number three," said Rida Issa, using an Arabic acronym for IS.
"The final battle for Sirte has started," said the spokesman for forces backing the Tripoli-based Government of National Accord.
About 1,000 pro-GNA fighters were taking part in the offensive, he said, adding a tank had destroyed a bomb-rigged car before IS jihadists could use it to target the forces at the start of the assault.
The pro-GNA forces said on their Facebook page that the offensive came "after air strikes overnight by the warplanes of international support".
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Pro-GNA forces, backed since August 1 by US air strikes, began an assault in mid-May to expel IS from Sirte.
The jihadists seized control of the city, which had been the hometown of Libya's slain dictator Muammar Gaddafi, in June 2015.
The pro-GNA forces fought their way into Sirte on June 9 and seized the jihadists' headquarters at the Ouagadougou conference centre on August 10.
More than 350 pro-GNA fighters have been killed and nearly 2,000 wounded in the battle, according to medical sources. IS casualty figures are unavailable.
Sirte lies 450 kilometres east of Tripoli.