Citing the Ministry of Emergency Situations, the state-run TASS News Agency said that rescuers found 10 more bodies at the scene of the accident in Yeysk city, raising the death toll to 13, including three children.
Nineteen others were injured and sent to hospital for treatment, Xinhua news agency quoted the TASS report as saying.
During the rescue process, 68 people were rescued, and 360 people were evacuated to safety.
Earlier reports said the aircraft collapsed while it was gaining altitude during a training flight from an airfield of the Southern Military District, and the pilots were able to eject safely before the crash.
The crew had reported that an engine caught fire during take-off.
TASS reported that the plane burst into flames, spreading to a nine-story residential building nearby.
It also said that the accident caused damage to 17 apartments, with the fire reaching an area of 2,000 square metres.
Russian authorities have launched an investigation into the cause of the accident.
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