A two-week-old government-backed offensive has now killed 254 people, the medical sources said.
At least 36 died on Friday and Saturday, when loyalists of former general Khalifa Haftar and regular army troops attacked Islamist militiamen in east and south Benghazi.
The pro-government forces recaptured military positions that the Islamists, including the radical Ansar al-Sharia group, had seized in July, the military sources said.
A spokesman for Libya's special forces said the unit took back its headquarters on the road to Benghazi airport, in the city's southeastern Bouatni region.
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Armed forces general staff spokesman Colonel Ahmed al-Mesmari said the entire east of Benghazi was now back under the control of government troops, while pro-government forces were making advances in the south of the city.
Witnesses said Haftar loyalists backed by government troops and armed civilians seized several homes owned by Islamists and destroyed some of them.
Air strikes targeted several neighbourhoods, including the Islamist stronghold of Al-Gawarsha in the west, witnesses said.
They said the government troops had been deployed in several parts of the eastern city for the first time since July.
Islamist militias, including Ansar al-Sharia which is blacklisted by Washington as a terrorist group, have held sway in most of Benghazi since July.