A view of the damaged apartments after a warplane crashed into a residential area in Yeysk, Russia, on Tuesday. AP

The ministry of emergency situations said in a statement that rescuers had completed the search of the rubble, and discovered "10 more bodies", after earlier announcing three deaths.

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"In total, 13 people died, including three children, while 19 people were injured," according to the ministry, as quoted by Russian news agencies.

The Sukhoi Su-34 crashed on Monday evening, causing a massive fire that engulfed a nine-storey building where around 600 people lived.

Firefighters work at the scene after a warplane crashed into a residential area in Yeysk, Russia, on Monday. AP

Russian President Vladimir Putin was informed of the fire and ordered "all necessary assistance be given to casualties from the military plane incident", the Kremlin told the state-run TASS news agency.

"At the site of the Sukhoi Su-34 crash, in the courtyard of a residential area, the aircraft's fuel caught fire," the ministry of defence said.

Images on social media showed a Soviet-era residence block engulfed by flames.

The blaze spread over five floors of the building, covering 2,000 square metres (21,500 square feet), the ministry of emergency situations said.

The defence ministry said the plane's pilots were able to eject.

The plane crashed after taking off to carry out a training flight from the military airfield of the Southern Military District, it said.

It added that the military jet had malfunctioned after "one of its engines caught fire during take-off".

Agence France-Presse