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The secretariat in a statement said the Air Force Learjet 45 crashed after it took off at around 15:45GMT from Emiliano Zapata in Veracruz State.
The statement added that the Accident Investigation Commission will join the army and air force to “carry out the corresponding expert reports to determine possible causes.”
The statement did not give details concerning the identity of the military personnel, or reasons they were aboard the flight.
“We express our deepest condolences to our comrades in arms,” said the secretariat.