Forces loyal to Libya's military strongman Khalifa Haftar have retaken most of the coastal city since it was overrun by jihadists in 2014.
Forces loyal to Haftar, who does not recognise a UN-backed unity government in Tripoli and backs a rival parliament, have retaken most of the coastal city since it was overrun by jihadists in 2014.
Riadh Chehibi, an officer in Haftar's self-styled Libyan National Army, said the forces advanced in the central district of Al-Sabri and Souq al-Hout area near the port, where jihadists are surrounded.
Haftar's forces retook certain positions from the jihadists, but reported no casualties among their ranks, Chehibi said.
Footage and pictures shared online showed columns of tanks, armoured vehicles and ambulances heading towards the neighbourhoods.
Many jihadists found refuge in Al-Sabri and Souq al-Hout after the LNA drove them from the city's western districts in March.
In April, the military authorities in Benghazi asked civilians living near these districts to leave their homes to avoid being caught in the crossfire.
Jihadists groups in the city include the Revolutionary Shura Council of Benghazi, an alliance of Islamist militias among them suspected members of the Islamic State group and the Al-Qaeda-linked Ansar Al-Sharia.
In another video being shared online on Monday, an LNA officer is shown shooting dead a man said to be a suspected IS member from Algeria.
The footage shows the officer holding his gun to the head of the prisoner, who is kneeling down with his hands on his head.
In March, rights group Human Rights Watch said Haftar's forces may have committed war crimes as it fights jihadists in Benghazi.
The LNA repeatedly denied the claims, but a top official for the special forces in the city, Wanis Boukhamada, then came forward to denounce the abuses and promised to try and punish those responsible.
Libya has been wracked by chaos since the 2011 uprising that toppled and killed longtime dictator Moamer Kadhafi, with rival authorities and militias battling for control of the oil-rich country.