A further 20 people were injured and the number of fatalities could rise, Fadia al-Barghathi, spokeswoman for the city's al-Jala hospital, told AFP.
An explosives-rigged vehicle blew up in front of a mosque in the central neighbourhood of Al-Sleimani, a security source said.
A second car exploded 30 minutes later in the same area, causing more casualties among security services and civilians.
Libya has been rocked by chaos since a 2011 uprising that toppled and killed dictator Moamer Kadhafi, with two rival authorities and multiple militias vying for control of the oil-rich country.
Military strongman Khalifa Haftar in July announced the "total liberation" of Benghazi, three years after his forces launched a military operation to seize the city from jihadists who had made it a stronghold following the revolution.
But clashes and attacks in the city have continued, including against diplomatic facilities and security forces.
Haftar supports a parliament based in the far east of Libya, while a rival United Nations-backed unity government in the western capital Tripoli has struggled to assert its authority nationwide.
