Deputy Defense Minister Khaled al-Sherif said Barghati's "bodyguards traded fire with angry soldiers and ex-rebels but the minister was not hurt" in an attack near the Tobruk airbase just east of Benghazi, the Tripoli Post reports.
The Defense Ministry said Barghati was in the region discussing security issues with the Libyan military. The newspaper cites anonymous military officials who said fighting began shortly after the government decided to eliminate a ministerial post for the country's national guard.
Libyan Prime Minister Ali Zidan is reportedly considering imposing a curfew in Benghazi due to recent security incidents, the newspaper adds.
The Italian government recently announced it was closing its diplomatic outpost in Benghazi after the Italian envoy to Tripoli was attacked, but uninjured, after he left the consulate's grounds there.
U.S. Ambassador to Libya Chris Stevens and three members of his staff died when militants attacked the U.S. consulate in Benghazi in September. U.S. Secretary of State Hillary Clinton is to testify before a U.S. Senate committee about the incident this week.