The two attackers, who detonated car bombs, targeted a Libyan army special forces barracks in the Bouatni area of Benghazi, an army official told AFP.
A medical official said the blasts yesterday killed four people, not including the two attackers themselves, as well as an "unknown number of wounded".
The attack hit just as the men were breaking the fast for the Muslim holy month of Ramadan, the military source added, saying that a bomber on a lorry forced his way onto the base before detonating the vehicle.
No group claimed the double bombing, which came a day after deadly clashes between the army and Islamist groups.
At least 16 people, mostly soldiers, were killed and 80 wounded in the clashes.
Parts of the eastern city of Benghazi have become strongholds for Islamist groups since the 2011 revolution that ousted longtime dictator Muammer Gaddafi.