"We have found the Algerian plane. The wreck has been located ... 50 kilometres north of the Burkina Faso border" in the Malian region of Gossi, said General Gilbert Diendiere of the Burkina Faso army.
A witness had earlier reported seeing the plane "falling" in the region of Gossi and the general said they were taking the reports seriously as they matched radar images of the flight path.
Flight AH5017, which originated in Ouagadougou and was bound for Algiers with 51 French nationals aboard, according to Foreign Minister Laurent Fabius, went missing amid reports of heavy storms, company sources and officials said.
It had been presumed to have been lost even before Fench President Francois Hollande went on TV to announce: "Everything leads us to believe that the plane has crashed."
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He said the plane's Spanish crew had signalled they were altering course "due to particularly difficult weather conditions".
Algerian Prime Minister Abdelmalek Sellal was earlier cited as saying by Algerian radio that the plane dropped off the radar at Gao, 500 kilometres from the Algerian border.
The airline said it also had 24 Burkinabe, eight Lebanese, six Algerians, six Spanish, five Canadians, four Germans and two Luxembourg nationals on board.
Mali, Algeria, Niger and France coordinated their search efforts under the umbrella of the French-led military intervention in Mali, Operation Serval.
"Even though the aircraft was above Mali it was in airspace managed by the control centre in Niamey in Niger," an air traffic control official told AFP.
Its six-member crew were all Spanish, said Spain's airline pilots' union Sepla, and Swiftair confirmed the aircraft went missing less than an hour after takeoff.
The plane had apparently been given the "all clear" following an inspection in France only this week, the French civil aviation authority DGAC said.