"The cultural attache and three other staff were kidnapped in Tripoli," ministry spokesman Said Lassoued told AFP.
The early morning abduction came a day after the seizure of an embassy administrative adviser from his home in the capital and despite Libya's announcement of "reinforced security measures" around the Egyptian embassy.
A security official would not rule out that the earlier kidnapping was a response to the arrest in Egypt yesterday of a prominent former rebel commander who fought in the 2011 uprising against Muammar Gaddafi.
The presidency of the General National Congress, Libya's highest political authority, ordered the ambassador in Cairo to demand an explanation of Hadeia's arrest and seek his immediate release.
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Libya has been struggling to integrate the rebel groups that helped topple the Kadhafi regime into the regular armed forces. Militias have carved out their own fiefdoms, each with its own ideology and regional allegiances.
There has been a spate of attacks on foreign missions as well as Libyan security personnel, some blamed on groups inspired by al-Qaeda.