The fiery crash of an ageing Boeing passenger jet close to Havana's main airport killed 110 people while three survivors remain gravely ill in hospital, officials have said, making it the Caribbean island's deadliest air disaster in nearly 30 years.

The initial death toll from state-run airline Cubana's stricken Flight 972 was 103. But Cuba's transportation minister confirmed that number had now risen.

It came as investigators said they had retrieved the black box cockpit voice recorder, which may offer clues to the as-yet unanswered questions about why the Boeing 737 crashed.

Skies were overcast and rainy at the airport at the time of the accident and state television said the 39-year-old jet veered sharply to the right after departing on a domestic flight to the eastern city of Holguin.

Eyewitness Rocio Martinez said she heard a strange noise and looked up to see the plane with an engine on fire.

"In flames, here it comes falling toward the ground and it seems (the pilot) saw it was an area that was too residential and makes a sharp turn," Ms Martinez said. "To avoid (the houses) ... to avoid a tragedy, because there would have been a massacre."

Among the dead are 20 clergy members of an evangelical church and the Mexican pilots and cabin crew.

Commenting on the three female survivors, Carlos Alberto Martinez, director of Havana’s Calixto Garcia Hospital, said: "We must be conscious that they present severe injuries. They are in a critical state."

A firefighter works in the wreckage of a Boeing 737 plane that crashed in the agricultural area of Boyeros, around 12 miles south of Havana (Reuters)

Cuban President Miguel Diaz-Canel said a special commission had been formed to find the cause of the crash. The plane had 113 people on board, including six crew members.

State airline Cubana, which operated the flight, has had a generally good safety record but is notorious for delays and cancellations, and has taken many of its planes out of service because of maintenance problems in recent months, prompting it to hire charter aircraft from other companies.

Mexican officials said the Boeing 737-201 was built in 1979 and rented by Cubana from Aerolineas Damojh, a small charter company that also goes by the name Global Air.