ISIL is understood to have been restricted to a shrinking residential area in the centre.
At least nine Libyan brigade fighters were killed and dozens wounded in some of the latest fighting, on Sunday.
Video shows a courthouse that had been run by ISIL, with their black flags painted on some walls.
The Libyan forces are aligned to the UN-backed unity government, based in Tripoli.
Mainly from Misrata, they have been supported by US air strikes since the start of this month.
The militants control of Sirte last year and losing it would be a major blow.
But those who have escaped or who are based elsewhere are likely to keep fighting, amid Libya’s continuing political turmoil and security vacuum.
On Monday, there was a setback for the beleaguered unity government, when opponents voted to reject it in a rare session of the eastern-based parliament.
But some of the government’s supporters dismissed the move as unconstitutional.
The Government of National Accord (GNA), the product of a UN-backed deal signed in December, has been seeking endorsement for months as it tries to extend its influence and authority beyond its based in Tripoli. (Euronews)