Seven children were killed, along with nine women and eight men. A 9-year-old child was among four people who survived the Saturday afternoon crash.
Relatives of the survivors told local media that one of the engines apparently stopped just before the pilot tried an emergency landing in the Manacapuru river.
The survivors "opened the rear door and left the plane while it was submerging," Walcione Tavares told Globo TV. Rescuers reached them at the scene later Saturday.
Another relative, Roberto Buchdid, said his wife called and told him to alert authorities.
"She was very scared," Buchdid said.
The plane belonged to the Manaus Aerotaxi and was making a 185-mile (300-kilometer) flight from the city of Coari to Manaus, the capital of Amazonas state.
Manaus Aerotaxi director Fernando Bezerra said the aircraft had undergone all of its scheduled maintenance inspections. Brazil's Civil Aeronautics Agency -- known as ANAC -- said the plane's documentation was up to date.
The Brazilian air force said the flight plan showed 20 people were on board, but some of the children may not have been listed.
O Globo newspaper, citing Brazilian aviation officials, said the pilot contacted air controllers to report encountering driving rain. But he did not specifically mention an engine malfunction, the paper said.
Authorities were still investigating, and it was not clear if any tourists were on board.
Local media cited local police officers saying the flight was packed with members of a family heading to Manaus to celebrate a relative's birthday.
Eight rescue divers remained at the scene preparing the plane to be removed from the river. Braga said it was only partially damaged.
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