General Abdelrazak al-Nadhuri “escaped unharmed from a terrorist assassination attempt after a car bomb exploded… as his convoy passed,” the LNA said in a statement.
The explosion took place in the Sidi Khalifa district at the eastern entrance to Benghazi, the statement said.
One civilian was killed in the attack and another injured, a spokesman for Benghazi’s al-Jala hospital told AFP.
Nadhuri’s spokesman Malek al-Sharif told AFP that the chief of staff, his bodyguards and those travelling with him were unharmed.
The attack comes after Haftar, who supports an administration based in the far east of Libya, was in hospital in Paris last week after falling ill during a trip abroad.
The strongman has not many any public appearance in the past two weeks and social media has been abuzz with rumours.
After several denials, the LNA acknowledged Friday that Haftar had been hospitalised but was “in good health”.
Libya has been gripped by chaos since a NATO-backed uprising toppled and killed longtime dictator Muammar Gaddafi in 2011, with rival administrations and multiple militias vying for control of the oil-rich country.
Last summer, Hafter announced the “total liberation” of Benghazi, after a three-year campaign to seize the city from jihadists who had made it a stronghold following the revolution.
Haftar supports a parliament based in the east of the country, while a UN-backed unity government in the capital Tripoli has struggled to assert its authority nationwide.
The Islamic State group remains active in central and southern Libya despite being forced out of their northern stronghold Sirte in 2016.