Simultaneous attacks on UN-backed government come just hours after suspected Egyptian jets target areas south of Sirte.
East Libyan forces say they have gained control over one of two key remaining districts in Benghazi where they had faced armed resistance.
The advance in the central Souq al-Hout neighbourhood on Saturday was the latest step in the slow progress of the self-styled Libyan National Army (LNA) commanded by Khalifa Haftar, which is aligned with the Tobruk-based House of Representatives and refuses to recognise the UN-backed government in Tripoli.
In unusually heavy fighting in Benghazi over the past two days, at least 13 men from the LNA were killed and 37 wounded, a medical official said.
Many of those who died were killed by landmines, a military source said.
Along with Sabri, Souq al-Hout was one of the final holdouts of the LNA’s rivals.
Since 2014, shifting alliances have been battling for power. The LNA and the eastern Libya-based government have rejected a UN-backed Government of National Accord (GNA) that has been in the capital, Tripoli, since last year.
Saturday’s advance came after the Benghazi Defence Brigades (BDB), an anti-Haftar armed group that includes fighters who retreated from Benghazi and have since tried and failed to advance again towards the city, said it was prepared to disband and be integrated into national security forces.
Haftar forces have taken significant ground in eastern and central Libya over the course of the past year, including military bases, cities and oil facilities.
The UN’s Libya Sanctions Committee report, released on Friday, reveals the UAE has supplied attack helicopters and other military aircraft to Haftar’s forces.
“The United Arab Emirates have been providing both material support and direct support to LNA, which have significantly increased the air support available to LNA,” said the report by a UN panel of experts.
The report provides rare insight into foreign funding of armed groups in Libya, which many say has exacerbated the conflict.
It shows there has been an uptick in direct foreign support to armed groups in Libya, despite a UN embargo imposed on the country during the 2011 uprising and tightened in 2014.