"Our forces are advancing inside parts of district Number Three where the Daesh remnants are entrenched," the media centre of the campaign said in a statement, using an Arabic acronym for IS.
It came shortly after Reda Issa, a spokesman for the loyalist forces, said pro-GNA fighters were preparing for the last battle.
"Preparations to liberate the entire city are ongoing today and we expect the situation to be resolved in a very short time," Issa told AFP.
The forces loyal to the Tripoli-based Government of National Accord launched an offensive more than three months ago to drive IS from Sirte, and they have been backed by US air raids for almost a month.
After capturing most of the city including IS's central headquarters earlier this month, loyalist forces have cornered the jihadists in one last district further tightening the noose on the Muslim extremists.
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IS overran the Mediterranean hometown of Libya's slain dictator Moamer Kadhafi in mid-2015, sparking fears the jihadists would use it as a springboard for attacks on Europe.
On Sunday at least 38 pro-GNA forces were killed and 185 wounded in clashes with the jihadists after the loyalist fighters announced the "final battle" to retake the whole of Sirte.
By Monday night they had routed jihadists from district Number One in the north of the city with Issa telling AFP: "The price was costly but they liberated it."
Medical sources said at least 10 pro-GNA fighters were killed in Monday's fighting.
Loyalists have said they have poured 1,000 fighters in the offensive launched at the weekend.
More than 400 loyalist fighters have been killed and nearly 2,500 wounded in the battle for Sirte since May, medical sources say.
IS took advantage of the chaos in oil-rich Libya after the 2011 uprising that toppled and killed Kadhafi and seized Sirte in June 2015, hoisting their black flag above the city.