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.

"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.

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".

- Investigation opened -

Regional governor Veniamin Kondratyev told reporters his administration was "providing maximum assistance" to residents and promised to "figure out whether the house would be restored, or we will build new apartments."

The fire was brought under control by 1730 GMT Monday, he said.

Kondratyev earlier said on Telegram that the fire had spread to a few floors and that 17 flats were affected.

Russia's investigative committee, which looks into serious crimes, said it had opened a criminal investigation into the crash.

Since the beginning of the Ukraine offensive, the airspace around the south of Russia has been closed.

Yeysk town is on the Taganrog Gulf on the Sea of Azov, opposite the Ukrainian city of Mariupol, which is under Russian control after relentless bombardment and a long siege.

Oksana, a resident who declined to give her last name, said the area had been cordoned off.

"There could be an explosion. Everything is burning inside. There is smoke," she told AFP.

She said she was stuck in traffic when she heard the news.

"I'm in shock obviously. My child was alone at home. We already used to go to sleep with fear every day -- Mariupol is just across from us," she said, referring to the nearby Ukrainian port besieged earlier this year by Russian forces.

Accidents involving Russian civilian aircraft and warplanes are fairly common, usually caused by technical malfunction or human error.

In June a military plane crashed in the city of Ryazan, southeast of Moscow, killing four people and injuring five others.