There were three seriously injured survivors, Cuban president Miguel Diaz-Canel said. On visiting the site of the crash, he told Agence France Presse: "It appears there is a high number of victims."
"We heard an explosion and then saw a big cloud of smoke go up," said Gilberto Menendez, who runs a restaurant near the crash site in the agricultural area of Boyeros.
According to witnesses, a massive fireball followed by a towering stack of smoke was visible near the airport on the outskirts of the Cuban capital. Radio Habana Cuba, a state-run frequency, reported the aircraft crashed near a motorway about 30 kilometers from downtown Havana.
"The plane fell in pieces of iron and other materials on a field of sweet potatoes, 200 meters from the first buildings... cars were set on fire, and a score of ambulances rushed to the spot," one AFP reporter said.
Cubana de Aviacion, Cuba's national carrier, reportedly leased the aircraft from Mexican airline Damojh.
A Damojh representative told Reuters in Mexico: "There is still no information, we are gathering what we can to give correct information. As the day progresses there will be more information."
The Mexican government said on its website that the plane was a Boeing 737-201 built in 1979, making it around 39 years old.
Boeing Co said in a Twitter post: "We are aware of news reports out of Cuba and are closely monitoring the situation."
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