Militias aligned with the new Government of National Accord (GNA) are being backed by air strikes and bombardment from naval ships as they fight to dislodge militants from the city centre.
Leaders said senior Isis members had fled into the desert to the south, while there were reports of the group’s fighters shaving off beards and cutting their hair in attempts to blend in with displaced civilians.
But hundreds of militants are believed to remain in Sirte, lying in a strategic position on Libya’s Mediterranean coastline, and street battles continued on Saturday.
Clashes were focused on the Ouagadougou conference complex, which was built by deposed Libyan leader Muammar Gaddafi but has since been used as an Isis command centre and venue for religious instruction and propaganda videos.
Brigades largely composed of fighters from Misrata advanced to the edge of the city centre this week, after launching a counter attack against the so-called Islamic State last month and driving militants back along the coastal road between the two cities.
A source from the operations room told Reuters fighters from front lines in the south of Sirte had looped round along the seafront to capture the port, which lies about three miles east of the city centre.
The brigades have advanced more swiftly than many expected, though their progress has been hampered by suicide bombers, mines, booby-trapped vehicles and Isis snipers.
Mohamed al-Gasri, a military spokesperson based in Misrata, told Reuters: “We think that Sirte will be liberated within days, not weeks.”
In pictures: Isis' Libyan stronghold of Sirte
In pictures: Isis' Libyan stronghold of Sirte
1/10 Isis in Sirte
Isis fighters parade through in Sirte in 2015
2/10 Isis in Sirte
Islamic State (IS) group jihadists on the outskirts of Libya's western city of Sirte
3/10 Isis in Sirte
A photo of a billboard in Sirte, Libya, listing seven rules for women's clothing, saying they must be loose-fitting and undecorated
4/10 Isis in Sirte
Isis militants process down a street in the coastal city of Sirte in Libya this week; the group has heralded Libya as its ‘strategic gateway’ to attack Europe
5/10 Isis in Sirte
An Isis lecture on Sharia at the Ouagadougou complex in Sirte, Libya, in 2016.
6/10 Isis in Sirte
A sign reading "The city of Sirte, under the shadow of Sharia" as smoke rises in the background while forces aligned with Libya's new unity government advance on the eastern and southern outskirts of the Islamic State stronghold of Sirte on 9 June.
7/10 Isis in Sirte
Fighters loyal to Libya's GNA prepare to launch attacks against Isis as they continue their resistance on the outskirts of the western city of Sirte
8/10 Isis in Sirte
Forces loyal to Libya's UN-backed unity government are seen during clashes with jihadists of the Islamic State (IS) on the western outskirts of Sirte on June 2, 2016.
9/10 Isis in Sirte
Forces loyal to Libya's UN-backed unity government fire during clashes with Isis around 14 miles west of Sirte on June 2, 2016.
10/10 Isis in Libya
A separate militia that controls terminals in Libya's oil crescent, the Petroleum Facilities Guard (PFG), said it was advancing towards Sirte from the east after reaching the town of Harawa, about 40 miles away.
Several symbolic and strategic locations have been retaken, local media reported, including the Saadi barracks, where the bodies of executed Isis fighters were allegedly found, the Mahari Hotel and a roundabout where militants previously hung the bodies of killed civilians.
At least 11 fighters were killed and 35 wounded on Friday, pushing the death toll over 100 for GNA-backed groups since operations began in May.
Isis claimed it had killed dozens of enemy fighters in recent days but has not released any statements acknowledged any retreat through official propaganda channels, instead posting footage claiming to prove it is still in control of some areas.
Sirte was Gaddafi’s hometown and the scene of his death, during the last major battle of the Libyan civil war in 2011.
Isis took advantage of the ensuing chaos to expand into the country, seizing Sirte and 155 miles of surrounding coastline in late 2014 to construct its biggest stronghold outside Syria and Iraq.
Civilians trapped by the terrorist group have reported “unbearable” atrocities, including regular public executions and corpses left hanging or “crucified” in the streets.
Pro-government militias have been the main fighting force for the UN-brokered unity government formed earlier this year in efforts to stem the bloodshed and chaos following Gaddafi’s death.
They are being supported by the UK and other nations including the US, which sending a second aircraft carrier and its strike group of guided-missile cruisers and destroyers to bolster operations Mediterranean.
The Ministry of Defence told The Independent it could not comment on reports that British special forces were supporting militias in Sirte, alongside American and Jordanian teams.
The assault on Sirte comes as US-backed fighters in Syria converge on the Isis stronghold of Manbij on three sides, while Iraqi special forces push into the Iraqi city of Fallujah.
The so-called Islamic State has suffered setbacks on several fronts in the region where it captured large swathes of territory two years ago, including the loss of the ancient Syrian city of Palmyra.