Russian President Vladimir Putin today visited the scene of a fire in a shopping mall that killed at least 64 people, and hit out at "criminal negligence" which he said was to blame for the high death toll.

Investigators looking into a fire, one of the deadliest in Russia since the break-up of the Soviet Union, said fire exits at the mall had been illegally blocked and the fire alarm system had not functioned properly.

Russian President Vladimir Putin meets with locals and relatives of persons missing in a fire in a shopping mall in the Siberian city of Kemerovo, Russia March 27, 2018. Photo: Reuters

The fire swept through the upper floors of the Winter Cherry shopping centre in the city of Kemerovo, where a cinema complex and children's play area were located, on Sunday afternoon.

Dozens of children were feared to be among the dead in the tragedy in Kemerovo, a coal-producing region about 3,600 km (2,200 miles) east of Moscow. As well as grief, the fire has stirred public anger about apparent failures in fire safety standards at the mall.

Putin, re-elected last weekend, arrived at the scene on Tuesday and laid flowers at a makeshift memorial to the victims of the fire.

"What's happening here? This isn't war, it's not a spontaneous methane outburst. People came to relax, children. We're talking about demography and losing so many people," Putin said in a meeting with ministers in Kemerovo.

"Why? Because of some criminal negligence, because of slovenliness. How could this ever happen?" Putin asked.

The head of Russia's Investigative Committee, which handles major crimes, said the fire alarm system in the mall had been out of order since March 19 and a security guard had not turned on the public address system to warn people to evacuate the building.

The committee said earlier it was trying to bring in the mall's owner for questioning.

"Serious violations (of the law) took place when the mall was being built and when it was functioning. The fire exits were blocked," Svetlana Petrenko, a spokeswoman for the committee, said in a statement on Monday.

Four people have already been detained, including two employees of the firm that services the mall's fire alarm.

Emergency services said they had extinguished the fire, but later said it had re-ignited in places and that rescuers were struggling to recover bodies because the building's top floor had collapsed.

It was unclear whether any people were still unaccounted for.

Health Minister Veronika Skvortsova said from the scene that 13 people were in hospital, including an 11-year-old boy in a serious condition. Russian media said the boy had leapt from a window and that both his parents had been killed.

Many of the victims will only be identifiable by DNA testing, officials said.

An unofficial list of those missing circulating on Russian media included more than 20 children, some as young as five.

Mobile phone messages sent from one of those on the list, 13-year-old Maria Moroz, and published by Russian media, said: "We are burning. I love you all. This is perhaps farewell."