The report also says that an additional 43 people have been injured in the blaze.
"There are no accurate lists", the television reporter said, "but the parents are holding on to the hope that the names of their children will be moved from the list of the dead to those missing". At least 10 were hospitalized, and about 200 animals in a mall petting zoo died, officials said.
There was no immediate indication of the cause of the fire.
The Investigative Committee says a fire safety technician at the complex "switched off the alarm system" after being alerted about the fire.
Russian shopping mall fire kills 64; no alarms reported
The news agency had earlier reported that 11 of the bodies had been found in the mall's cinema.
It was the deadliest blaze in Russian Federation in recent years.
Lillevyali told the Meduza news website that one of his daughters called him, saying that they could smell the smoke but could not get out because the door was locked. A woman wrote on Instagram that somebody shouted "fire!" while she was watching a movie but that the film played on as panicked people rushed for the only door that could be opened.
In a statement, Alexandre Eremeyev - an official with the local Russian emergency services ministry - said: "This shopping centre on several floors was packed with people midday Sunday".
Five suspects have been arrested over the case, including the head of the management company, servicing the shopping mall, and the head and an employee of the mall's private security company.
Some were quick to blame lax regulations on Russia's fire safety inspection authorities, who have been accused of taking bribes to turn a blind eye to breaches.
The UN Secretary General Antonio Guterres wished speedy recovery to the wounded and extended his deepest condolences to the families of the victims and to the people and government of Russian Federation.
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Those cancellations come ahead of a separate strike by Air France pilots and cabin crew Friday seeking a six-per cent raise. The Paris Metro was running normally, but suburban trains were affected by the strike.