MOSCOW — At least 37 people died when a fire burned through a shopping mall in the Siberian city of Kemerovo on Sunday, the Russian authorities said.

Many of the victims were children, and at least 29 people were still missing after the blaze in the industrial city of about half a million people, over 2,000 miles east of Moscow, the Interfax news agency reported. The missing had little chance of survival, it said, citing a source in the rescue team.

The fire started around 5 p.m. on the fourth floor of the mall, which includes a three-screen cinema complex, a skating rink and an entertainment center for children.

Speaking to the relatives of the missing, Vladimir Chernov, a deputy governor of the Kemerovo region, said the fire had started in the children’s entertainment room, where there was a trampoline with foam rubber.

“The preliminary version is that one of the children had a lighter,” Mr. Chernov told the relatives, according to Interfax. “The fire started from the trampoline pool, filled with foam rubber, which got lit up as gunpowder.”

Mr. Chernov said that the fire alarm then did not work and that the cinema hall’s doors were shut.

The Investigative Committee, Russia’s equivalent to the F.B.I., said it had opened a criminal investigation into the cause of the fire.

Initial reports said that five people had died, but the death toll began quickly rising in late evening. The fire was still raging after midnight.

Thirty-six people were hospitalized, according to the state-run news agency Tass.

Videos of the fire posted on social media showed plumes of smoke billowing from the mall’s roof and windows. Other videos showed people jumping from windows to escape the flames and smoke.

President Vladimir V. Putin expressed his condolences to the relatives of the victims.

Russia has been the scene of numerous such deadly fires. More than 100 people died in a fire at a nightclub in Perm in 2009.