Forces allied to the Tripoli government assert they now have the upper hand.
Warplanes bombed IS positions in Sirte while naval forces fired missiles into key areas including the port that are held by the militants, officials say.
The battle for the city began last month but has recently intensified.
Libya still has rival regional administrations and armed forces in the east and west of the country, with each battling extremist militants in their territories.
The forces spearheading the advance on Sirte are the Tripoli-based UN-backed Government of National Accord (GNA).
Coastguard commander for central Libya Col Reda Issa told the BBC that his men were now positioned across Sirte's coastline to prevent any militants from trying to escape.
He said they had fired missiles from the sea targeting at least four key positions held by militants there, including the port.
A spokesman for ground forces battling IS militants described Thursday's fighting as "guerrilla warfare".
He said troops were on the fringes of residential areas in the city centre, but sniper fire and explosive devices planted by IS were slowing down the advance.
Sirte is IS's most significant stronghold outside Iraq and Syria. It is also IS's most valuable asset inside oil-rich Libya.
Local militias affiliated to al-Qaeda in April pushed IS forces out of their other base in the eastern city of Derna.
Fighting is also reported to be raging around the town of Harawa, about 70km (44 miles) east of Sirte.
Significant gains have been made by Libyan government air, sea and land forces fighting to recapture the central city of Sirte from so-called Islamic State, officials say.