Forces loyal to Libya's Government of National Accord said they have seized a new sector near the Islamic State of Iraq and the Levant group's command centre in Sirte.
The pro-GNA forces have been engaged in a military operation since May 12 to retake the coastal city, which lies 450 kilometres east of Tripoli.
Sirte has been an ISIL stronghold since June last year. Last week, United States forces started bombing ISIL positions in Libya.
The US says it is carrying out the air strikes at the behest of the GNA.
On Monday, the loyalists said that they had seized an area of guest houses close to the Ouagadougou conference centre, the complex from the era of slain leader Muammar Gaddafi where the ISIL fighters have their headquarters.
Pro-GNA forces entered Sirte in June, but their progress slowed as they were hit back with sniper fire, suicide attacks and car bombings.
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Since Thursday pro-GNA forces have been battling to reach the conference centre.
"Our forces have targeted Daesh snipers and their mines," the statement said, using an Arabic acronym for ISIL, which is also known as ISIS.
The guest houses are east of the Al-Dollar district, which the pro-GNA forces took last week and where VIP guests attending events at the Ouagadougou complex used to be housed.
On Sunday, the loyalist forces said they would soon begin a final assault to retake Sirte from ISIL.
Libya has been in a state of chaos since the 2011 overthrow of Gaddafi, with numerous revolutionary militias formed along regional and ideological lines vying for power.
The United Nations, France, Britain and the US recognise the GNA as the legitimate government of Libya.
In the country's east, meanwhile, forces loyal to former general Khalifa Haftar and others are loyal to a government based in the far eastern city of Tobruk. They reject the authority of the UN-back GNA.
Source: Al Jazeera and agencies