Forces loyal to Libya's UN-backed unity government pushed into the last areas of Sirte held by the Islamic State group in what was the jihadists' coastal stronghold.
The battle for the hometown of Libya's slain dictator Moamer Kadhafi was launched more than three months ago by forces loyal to the Tripoli-based Government of National Accord.
IS captured the Mediterranean city in June 2015, sparking fears they would use it as a launchpad for attacks on Europe.
"The final battle for Sirte has started," said Reda Issa, a spokesman for the pro-GNA forces, as loyalist forces thrust into two districts of the city where IS still holds positions.
About 1,000 pro-GNA fighters were taking part in the offensive against "district number one and district number two," in northern and eastern Sirte, he said.
An AFP photographer saw several tanks and armed vehicles move towards district number one and heard gunfire and rocket explosions as they entered the area.
"Fierce street battles" took place during the day with pro-GNA forces using weaponry including heavy artillery, the photographer said. He said the fighting later became more sporadic.
Late Sunday, a loyalist field commander, Hisham Abdel Atti, said pro-GNA forces had seized "two thirds of district number one and large parts of district number three."
The jihadists are "retreating," he said in remarks carried by the media center dedicated to the Sirte offensive.
At least 34 loyalists were killed on Sunday and 150 wounded, a field hospital for the pro-GNA forces said.
The AFP photographer saw several wounded men being evacuated to the field hospital.
The bodies of two IS fighters lay on a street inside district number one, he said.