Crews were still searching the Niger River for bodies late Saturday afternoon, said Ibrahim Maiga, who heads Radio Korondougou in Konna.
Survivors said that people from the nearby village of Kouri had rushed to the scene to help them.
Many of the passengers were school children returning to northern Mali ahead of the new academic year, said Abouri Djittey, a resident of Bamako whose 7-year-old daughter Ramata was among the dead. Others were traveling to visit relatives ahead of next week's Muslim holiday Eid al-Adha.
Large boats carry hundreds of people and cargo on the Niger River at this time of year, and the journey can take up to two nights and two days from Mopti to the fabled northern town of Timbuktu. Some vessels even transport two levels of passengers.
While most Malians cannot swim, travel by water is preferable to journeying on the poor roads across the country's desert north.
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Larson reported from Dakar, Senegal.