The forces, mainly brigades from the city of Misrata, say they are close to capturing Sirte after taking most of the city in a three-month campaign and restricting militants to a shrinking residential area in the city centre. Since Aug. 1, they have been supported by US airstrikes.
At least nine brigade fighters were killed and 85 wounded in Sunday's fighting, Misrata hospital spokesman Akram Gliwan said.
Fighters backed by heavy artillery and tanks advanced early in the day in Bufaraa neighborhood, seizing a building used by Daesh morality police as a prison, said Rida Issa, a spokesman.
Later, forces took Ribat mosque, Sirte's biggest, where senior militants, including leading Daesh ideologue Turki Ben Ali, had preached, the forces' media office said, Reuters reported.
The media office said "dozens" of bodies of Daesh terrorists were found in newly captured areas, although it did not give a specific number and it was not clear when the militants were killed.
As of Thursday, the United States had carried out 65 airstrikes over Sirte, according to US Africa Command, most recently against a supply truck, a vehicle-borne improvised explosive device and three enemy fighting positions.
The strikes have accelerated the progress of Libyan forces, whose advance had been slowed by suicide bombings, snipers and mines.
Daesh took control of Sirte last year, setting up a proto-state modeled on its practices in Iraq and Syria and enforcing its ultra-hardline rule on residents.
Losing the city would be a major blow for the group, although militants who escaped or are based elsewhere in Libya are expected to keep trying to exploit the country's political turmoil and security vacuum.