In a statement, the airport said the aircraft, a Fairchild Metroliner turboprop, was involved in an accident "upon takeoff."
"We can confirm that the five crew on board are deceased," it said, adding that the airport was closed until further notice and an investigation was underway.
Early media reports said the plane had been chartered by the European Union's border control agency, Frontex, for a flight to Libya.
Frontex issued a swift denial, and the EU's foreign policy representative, Federica Mogherini, said no European official had been onboard.
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