Fighters of Libya's unity government, backed by US air strikes, have recaptured more ground from jihadists holed up in the centre of the coastal city of Sirte, loyalist forces said Monday.

"Our forces have retaken the internal security building used as a prison by the Islamic State (IS)" group, as well as a courthouse, the Al-Naga district and Dubai Street, the operations centre for fighters loyal to the Government of National Accord (GNA) said.

A statement said "the new victory" was achieved in clashes which raged throughout Sunday in the face of "desperate resistance by the jihadists".

IS sniper positions were "neutralised" in two US air strikes and "our forces destroyed two booby-trapped cars... without loss in our ranks," it said.

However, 12 fighters were killed and 85 wounded in Sunday's clashes, the hospital in Misrata, 200 kilometres (120 miles) east of Tripoli where the pro-GNA military command is based, said on its Facebook page.

Pro-GNA forces, backed since the start of August by US air strikes, began an assault in mid-May to expel IS from what had been its Sirte stronghold.

The jihadists seized control of the city, which had been the hometown of Libya's slain dictator Moamer Kadhafi, in June 2015.

They fought their way into Sirte on June 9 and have since faced a barrage of sniper fire, suicide bombings and booby traps, pinning down the jihadists in a downtown area near the sea.

More than 350 pro-GNA fighters have been killed and nearly 2,000 wounded in the battle, according to medical sources. IS casualties figures are unavailable.

Sirte itself has been emptied of its residents, apart from families of IS militants, according to the pro-GNA forces.

American warplanes had carried out 65 strikes on IS positions in Sirte up until August 19, according to US Africa Command (AFRICOM).

Pentagon spokesman Gordon Trowbridge in mid-August estimated that jihadist fighters in Sirte numbered fewer than 1,000.