Authorities said 11 miners were found dead and three rescuers also died later while searching for others who were trapped at a remote section of the mine. Regional officials declared three days of mourning for the victims.
Kemerovo Governor Sergei Tsivilyov said 35 miners remained missing, and their exact location was unknown.
Efforts to rescue those trapped in the mine about 250 metres (820 feet) undeground were halted on Thursday afternoon because of an explosion threat, and rescuers were rushed out of the mine.
The Interfax news agency reported that miners have oxygen supplies normally lasting for six hours that could be stretched for a few more hours but would have expired by late hours Thursday anyway.
Nearly 50 other miners were injured.
A total of 285 people were in the Listvyazhnaya mine in the Kemerovo region in southwestern Siberia when the fire erupted and smoke quickly filled the mine through the ventilation system.
Russia's Investigative Committee has launched a criminal probe into the fire on charges of violating safety regulations that led to deaths.
President Vladimir Putin extended his condolences to the families of the killed miners and ordered the government to offer all necessary assistance to those who were injured.
Speaking at a meeting with his Serbian counterpart Aleksandar Vucic in the Russian Black Sea resort of Sochi, Putin noted that there is a danger to the life of the rescuers and voiced hope that they will manage to save as many people as possible.
In 2016, 36 miners were killed in a series of methane explosions in a coal mine in Russia's far north. In the wake of the incident, authorities analysed the safety of the country's 58 coal mines and declared 20 of them or 34% potentially unsafe.
The Listvyazhnaya mine wasn't among them at the time, according to media reports.
Russia's state technology and ecology watchdog, Rostekhnadzor, inspected the mine in April and registered 139 violations, including breaching fire safety regulations.
Another inspection of the mine was conducted Friday, but its conclusions weren't immediately reported.
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