Initial reports suggested it was caused by arson, claiming a child had a cigarette lighter inside a foam pit.
"The fire started from the trampoline room" - a children's zone in the complex,' said deputy governor Vladimir Chernov.
"The preliminary theory is that one of the children had a cigarette lighter.
"The fire started right in the foamed trampoline pool, which flared up like gunpowder."
Earlier reports from officials had failed to make clear the scale of the tragedy.
The fire will come as a severe blow to Vladimir Putin exactly one week after his landslide election victory.
He is currently facing a mounting diplomatic crisis over the poisoning of ex-spy Sergei Skripal in Salisbury as western countries fall into line behind Britain.
Mr Putin has ordered his emergencies minister Vladimir Puchkov to fly to Kemerovo to take charge of the disaster.
Firefighters early on Monday, local time, could still not reach the fourth floor of the gutted mall because temperatures were "too high".
Putin sent his "heartfelt condolences to the families and friends of the victims and wishes for a speedy recovery to the injured".
With several people still unaccounted for, a young girl, Vika, 12, called her family as smoke engulfed the complex. Now her fate is unknown.
Her aunt Evgenia said: "At about 16.11 I called my niece Vika. She told me: ''Everything is burning. The doors are blocked. I can't go out, I can't breath''.
"I told her: 'Vika, take off your clothes, cover your nose'.
"She told me: 'Aunty, tell all my family I love them. Tell mum that I loved her'.
The call ended with Evgenia not knowing if the young girl had made it out alive.
Evgenia added: "The school vacations have just began and almost all their class was there - about 10 people. Two or three parents and a teacher.
"The teacher left the kids in the cinema and went with parents in the shopping mall. So all the adults survived."
Another missing girl was Maria Moroz, 13, who disappeared with her mother Polina and friends in the same cinema that Vika was trapped.
The shopping complex is also home to a zoo, where all 200 of the animals are expected to have died.
Among them are rabbits, foxes, deer, wild pigs, goats, ferrets, meerkats, squirrels, hamsters and tortoises from a zoo inside the complex.
Director of the mall's pet zoo, Evgeny Videman, said he expected all his 200 animals had died.
"I think they were suffocated and died because I was the last to leave. There were no people left in the zoo.
"There was a strong smoke on the third floor, people were panicking on the side stairs.
"I just closed the doors. It was physically impossible to get the animals out.
"I am a vet and I guess that the animals are already choked with smoke."
The Russian Investigative Committee, which probes serious crime, confirmed: "Four children corpses have been found in a children's area during the rescue operations."
Earlier reports said children died from 'gas poisoning' in the mall.
Witnesses say there was no fire alarm in the centre.
Eyewitness Alexander Dorogov said: "Two floors went up in smoke in five minutes. The children's play area in the centre was engulfed in smoke in two minutes.
"The smoke was so thick that you couldn't see a stretched out hand. When firefighters came, two people had already jumped out of windows.
"We found some carpet to hold out and catch one of them."
In addition to concerns over gas poisoning, there were fears the burned shopping centre could collapse.
Fifteen fire teams, including 60 firemen were scrambled to the scene, where some 1,500 square metres of the mall was ablaze.
Videos show a jumper smashing into an awning over a door on the way down as onlookers screamed. The person is believed to have died from the fall.
Another shopper also jumped and was reported by witnesses to have survived when they were caught by people below.
Around 100 people were evacuated and 20 were rescued from the flames.
Parents were seen on videos ushering their children away from the scene.
