Three of the victims died when they jumped from the upper floors of the building in a desperate attempt to escape the flames, according to the vice governor of the region, Anna Menkova.
Fourteen people were killed after a Russian warplane crashed into a nine-story apartment building and ignited a massive blaze that engulfed several floors.
The Su-34 bomber came down in the Russian port city of Yeysk on Monday evening after suffering engine failure.
The Sea of Azov separates Yeysk and Russian-occupied territory in southeast Ukraine.
After hours of combing through the charred debris of the building, authorities said 14 residents, including three children, were found dead. Another 19 were hospitalised with injuries.
Vice governor of the region, Anna Menkova, said three of the victims died when they jumped from the upper floors of the building in a desperate attempt to escape the flames, according to the RIA-Novosti news agency.
The bomber came down 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, causing a fire as tonnes of fuel exploded on impact.
Authorities said they reserved emergency rooms and operating halls at local hospitals and scrambled medical aircraft.
At least 17 apartments were said to have been affected by the fire, and about 100 were said to have been evacuated.
The Kremlin said Russian President Vladimir Putin was informed about the crash and ordered the ministers of health and emergencies, along with the local governor, to head to the site.
On Tuesday, Russia's ministry of emergency situations said rescuers had ended their search for survivors in the rubble.
Russia's Investigative Committee, which probes serious crimes, said it had launched a criminal inquiry into possible violations of flight rules, and had "seized fuel samples at the departure aerodrome" and "flight recorders at the site of the crash".
Videos posted on Russian messaging app channels showed a massive fire engulfing an apartment building and loud bangs from the apparent detonation of the warplane's weapons.
Yeysk, a city with a population of 90,000, is home to a sizeable Russian air base and training centre.
The Su-34 is a supersonic twin-engine strike jet equipped with sophisticated sensors and weapons that has been a key strike component of the Russian air force.
It first flew in 1990, but it only entered into service 26 years later, in 2014. The aircraft has seen wide use during the war in Syria.
Russia was thought to have around 140 operational Su-34s prior to its full-scale invasion of Ukraine in late February.
Monday's accident marked the 10th reported non-combat crash of a Russian warplane since Moscow sent its troops into Ukraine.