Russian investigators opened a criminal probe. Some unnamed sources told Russian media they believed the plane had been shot down.
All ten people on board the aircraft died in the crash, according to the Russian Emergency Situations Ministry.
The first helicopter landed safely after the collision but the second one crashed, killing all three people who were on board.
A Russian Su-25 fighter-bomber crashed into the Sea of Azov on Monday.
"They have recovered size and weight, really they are very well," Astrid Caceres, the director of the country's child welfare institute, told journalists.
The National Transportation Safety Board will investigate the crash, the FAA said.
Researchers at MIT have developed new algorithms that could help human pilots deal with extreme near-crash events.
Rescuers, supported by search dogs, had previously found discarded fruit the children ate to survive, as well as improvised shelters made with jungle vegetation.
To this day, nobody knows why the small jet lost contact minutes after takeoff and crashed down to earth, four and a half hours later.
The reason for lack of response from the pilots remains unclear to authorities.
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