The death toll from the crash of a Russian warplane into a Russian city has risen to 15, including three people who died when they jumped from a nine-storey apartment building to escape a blaze, authorities said.

The Su-34 bomber went down on Monday in the Sea of Azov port city of Yeysk after one of its engines caught fire during takeoff for a training mission, the Russian Defence Ministry said.

It said both crew members bailed out safely, but the plane crashed into a residential area, igniting a huge fire as fuel exploded on impact.

After hours of combing through the charred debris, authorities said 14 people, including three children, were found dead.

Another 19 were taken to hospital with injuries, and one of them died of severe burns, bringing the death toll to 15, said Anna Minkova, a vice governor of the region.

Yeysk, a city of 90,000, is home to a big Russian air base.

The Su-34 is a supersonic twin-engine bomber equipped with sophisticated sensors and weapons.

It has been a key strike component of the Russian air force.

The aircraft has seen wide use during the wars in Syria and Ukraine.