MOSCOW — Emergency exits were blocked and a security guard had switched off the fire alarm system in a shopping mall in Siberia that burned on Sunday, preventing panicked people, including many children, from escaping the flames and smoke, the Russian authorities said on Monday.

At least 64 people died in the blaze in Kemerovo, an industrial city of about half a million people, more than 2,000 miles east of Moscow. Vladimir Puchkov, the emergency situations minister, said that six people were missing and 13 others hospitalized, including a teenager in grave condition.

The Investigative Committee of Russia, a law enforcement agency, said that four people involved in the ownership and maintenance of the building had been detained. The agency, Russia’s equivalent to the F.B.I., said that it had opened a criminal investigation into the cause of the fire, but that it was not clear whether anyone would be criminally charged.

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.

Some bodies were so badly damaged that the authorities may be able to identify them only through DNA, the Russian health minister, Veronica Skvortsova, said during a news briefing. She added that officials had started to take samples from relatives.

The mall will be demolished, Mr. Puchkov said.

On Monday, Russian news outlets reported heartbreaking stories from the scene of the fire. Aleksandr and Olga Lillevyali told Meduza.io, a news website, that their three daughters were in one of the cinema halls, watching the animated film “Sherlock Gnomes,” when smoke began to fill the room.

“My daughter kept calling me,” Mr. Lillevyali said, with tears in his eyes. “I only shouted to her that she should try to get out of the hall, but I couldn’t do anything — there was only fire in front of me.”

Some of the children trapped by the fire sent farewell messages through their social media accounts. Many were reportedly at the mall celebrating the start of their school break.

Speaking to 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. He said that the fire alarm did not work and that the cinema hall’s doors were shut.

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

Videos posted on social media showed black smoke billowing from the mall’s roof and windows, and people jumping from high windows to escape the flames, with nothing below to cushion their fall.

Fires in large buildings — including hospitals, a nursing home, and a nightclub — have been a recurring tragedy in Russia in recent years, often killing dozens of people.