The Russian Foreign Ministry said none of the embassy staff was wounded.
The Libyan official said the attackers yesterday, climbed the walls of the embassy compound from three different directions, firing in the air, and broke down its metal gate. The shooting wounded five, one of whom later died.
An attack last year on a US compound in the eastern city of Benghazi killed the US ambassador and three other Americans.
Russia's Foreign Ministry Ministry spokeswoman Maria Zakharova confirmed the attack, saying on Ekho Moskvy radio that according to preliminary information no one among the embassy personnel was wounded.
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The attackers were apparently reacting to the killing of a Libyan air force pilot Tuesday. Libyan authorities apprehended a Russian woman, accusing her of killing the pilot, then writing offensive graffiti in his blood. The woman later went on to stab and wound the pilot's mother, authorities say.
Libya has been hit by a months-long wave of targeted killings against activists, judges and security agents.
Yesterday, gunmen in Benghazi shot dead a naval officer and his 7-year-old son before fleeing the scene. Most killings are presumed to be the work of armed factions, often acting out of revenge.