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Police said 12 badly burned bodies were counted at the site, 70 kilometres (45 miles) north of the capital Antananarivo.
Hospitals said that 22 other deaths had been confirmed after the late-night crash.
“The bus struggled to climb a road on a hill and fell down a ravine about 20 metres deep,” police spokesman Herilalatiana Andrianarisaona told AFP.
“It caught fire after rolling several times.”
Photographs showed the white bus upside down and badly damaged, surrounded by burnt undergrowth.
The main hospital in Antananarivo said in a statement it had accounted for 18 dead, while a hospital in the town of Ankazobe near the crash scene reported four dead.
Passengers on the packed bus were travelling from the central town of Soavinandriana to a church meeting in the north-western coastal port city of Mahajanga when the accident happened.
Madagascan roads are often poorly maintained, with overloaded bus and trucks regularly involved in deadly accidents.
In January, 47 people, including 10 children and a newlywed couple, were killed when a truck carrying a wedding party and guests crashed.
The vehicle was transporting passengers the day after the wedding.
Madagascar, a French colony until independence in 1960, is one of the world’s poorest countries and relies heavily on international donors.
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