The source said the incident happened as Dbeibah was returning home, describing it as a clear assassination attempt, but the attackers fled and the incident has been referred for investigation.
Reuters has seen no immediate photographs or footage of the incident or its aftermath or spoken to other witnesses to the incident.
If confirmed, an attempt to assassinate Dbeibah could aggravate the crisis over control of Libya after he said he will ignore a vote scheduled by the eastern-based parliament later on Thursday to replace him.
Al Jazeera’s sources also said the bullets were fired from a light weapon, probably a Kalashnikov.
They said Libya’s chief prosecutor has launched an investigation into the attack.
RHM/PR