Sirte is the most significant IS stronghold outside Iraq and Syria, the BBC reports.
Air and missile strikes have hit IS positions this week, officials said. A spokesman said troops were moving closer to the city center.
The forces, aligned to the UN-backed unity government in Tripoli, began the battle to retake the city last month.
A spokesman, Ahmed Hadia, told the BBC IS forces had weakened, but "not totally broken down."
Read alsoReuters: Syrian government, U.S.-backed fighters advance against ISHe said the troops were encircling part of the city.
Clashes centered on the Ougadougou conference center, which was once a venue for international summits but has now become an IS command center.
Forces loyal to the government targeted the conference center with heavy artillery fire, backed by warplanes.
IS fighters responded using sniper fire, machine guns and mortar rounds.
The government said two soldiers were killed and eight were wounded.
The government spokesman told the BBC that troops were finding fewer landmines or booby-trapped cars the deeper they moved into the city.
Mr. Hadia said the car bombs they were finding were smaller than the ones they had used before, "which suggests they were hastily set up."
The troops' biggest fear, he added, was the presence of snipers and the possibility that civilians could be trapped in the battle zone.
Sirte was the hometown of ousted ruler Muammar Gadaffi.
The unity government was formed in Tripoli more than two months ago.
The U.S. said the unity government should be allowed to arm itself against IS. Secretary of State John Kerry has said this would be "the only way to generate the cohesion necessary" to defeat the militants.