Libyan rebel fighters are involved in heavy fighting in a final battle to capture Muammar Gaddafi's hometown of Sirte, one of the last three significant strongholds still held by the old regime.

Rebels are also advancing in strength on Bani Walid, a key tribal centre south of Tripoli, where the dictator's fugitive son Saif al-Islam is said to have been sighted in recent days. Reports from the rebel frontline described civilians leaving the town and explosions and heavy gunfire inside it.

Claims on Thursday night that Sirte had fallen to forces loyal to the National Transitional Council gave way to a standoff followed by renewed clashes on Friday morning. An al-Jazeera correspondent described heavy fighting and intense sniper fire around the industrial zone to the south-west of the town.

Sirte, on the coast between Tripoli and Benghazi, was hit repeatedly by Nato missiles and bombs from the start of the conflict in March, but has remained in the hands of Gaddafi forces since. If it does fall, the rebels will control Libya's entire Mediterannean coastline.

Yousif bin Yousif, a rebel commander from Misrata, told al-Jazeera that the entrances to the city were in their hands as elements of the 32nd Brigade – the elite unit commanded by Gaddafi's son Khamis – were holed up in villas on the coast. The rebels said they were expecting a last stand in the centre of town.

The Misrata rebel council said the Sirte attack was being mounted by 900 "technicals", flatbed pickup trucks mounted with machine guns or rocket launchers. Attempts were made to persuade Gaddafi forces – many from his Gadadfa tribe – to surrender but they responded by firing Grad rockets.

Bani Walid is the centre of the powerful Warfallah tribe. Its capture will leave only Sebha in the south, on the edge of the Sahara, in the hands of the old regime.

Amid mounting excitement about the latest military advances consolidating the February revolution, Libyans have been marking the 80th anniversary of the 1931 execution of Omar al-Mukhtar, hero of the resistance against Italian colonialists. Residents of Benghazi are planning a big rally to commemorate him.

Recep Tayyip Erdogan, Turkey's prime minister, has meanwhile arrived in Tripoli as part an Arab Spring tour that took him to Egypt and Tunisia earlier this week, and which he has been using to promote Turkey's ambitious regional role and to drum up business.

Turkish media reported complaints that the long-planned trip had been deliberately upstaged by Nicholas Sarkozy and David Cameron on Thursday.