The crash is Cuba’s worst air disaster in decades.
Three women were pulled alive from the wreckage, but are said to be in a critical condition.
The plane, which was nearly 40 years old, was carrying 104 passengers and six crew members.
Cuban authorities have launched an investigation, and two days of national mourning have been declared.
The Boeing 737-201 crashed at 12:08 local time on May 18, shortly after taking off from Havana on an internal flight to Holguin on the east of the island.
All six crew members on board were Mexican and the majority of the passengers were Cuban, with five foreigners reported to be among them.
Cuban President Miguel Diaz-Canel said after visiting the crash site: “There has been an unfortunate aviation accident. The news is not very promising, it seems that there is a high number of victims.”
According to authorities, it’s too early to say what caused the crash, but eyewitnesses on the ground describe seeing the jet burst into flames before crashing into a field close to a wooded area near Havana’s main airport.
Mexico’s transport department said on its website that “during take-off (the plane) apparently suffered a problem and dived to the ground”.
Boeing said that it was ready to send a technical team to Cuba, “as permitted under US law and at the direction of the US National Transportation Safety Board and Cuban authorities”. A US trade embargo has been in force against Cuba for many decades.
Four people survived the crash but one died after being transported to hospital, the director of Havana’s Calixto Garcia hospital, Carlos Alberto Martinez, told Reuters.
The three survivors are all women, according to Cuban Communist Party newspaper Granma: one aged between 18 and 25, one in her thirties and the third aged 39.
Both the Argentine and Mexican governments have confirmed nationals from their countries were among the dead.
The plane had been leased to state airline Cubana de Aviación by the Mexican company Aerolineas Damojh.
The Mexican authorities said the plane was built in 1979 and had been successfully inspected last November. Mexico has said it was sending two civil aviation specialists to join the investigation.
Aerolineas Damojh, also known as Global Air, has three planes in operation.
Cuba’s deadliest air crash was in 1989, when a Soviet-made Ilyushin-62M passenger plane crashed near Havana killing 126 people on board and another 24 people on the ground.
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