The plane plummeted into the ground shortly after take-off, killing the five French nationals on board.
The Maltese government said in a statement that there was no indication of an explosion prior to the crash but did not rule out sabotage, saying an investigation was under way into possible causes.
The French defence ministry said the plane had been working on its behalf, carrying out "reconnaissance missions in the Mediterranean".
Three of those who died were employees of the defence ministry, the two others worked for the company which flew the plane, the ministry said.
It took off around 7:20 am (local time). Shortly afterwards it was seen plunging nose-first towards the ground and exploding into a ball of flames.
"Official information, footage and eyewitnesses, including three members of the Armed Forces of Malta at the nearby barracks, and two commercial airline pilots, clearly indicate that there was no explosion prior to impact," a government statement said.
"The flight was part of a French customs surveillance operation which has been taking place for the past five months, with the aim of tracing routes of illicit trafficking of all sorts, including human and drug trafficking amongst others," the government said.
"The flight was registered with the Malta Air Traffic Services as a local flight and was to return to Malta within hours without landing in third countries."
Located just 220 miles (350 kilometres) north of Tripoli, Malta is on the frontline of Europe's efforts to contain the waves of migrants trying to reach Italy from Libya in boats operated by people smugglers who are often also involved in illicit drugs and arms dealing.
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