Investigators said fire exits had been illegally blocked, the public address system had not been switched on, the fire alarm system was broken, and children had been locked inside the cinemas.
Putin has also declared a nationwide day of mourning Wednesday.
Many locals do not believe the official death toll and suspect hundreds were killed and a cover-up is under way.
"Those workers who were supposed to be in charge of safety, organising evacuation, they were the first to flee", he told Putin.
The Kremlin transcript appears to have left out one telling statement that Tuleyev, the governor, made during the meeting with Putin, according to a video that is being widely shared on social media. A movie theater and children playing rooms were located on that floor. "Corruption!" the crowd chanted Tuesday at officials in the administrative buildings of Kemerovo.
Russian lawmaker Yelena Mizulina called the Kemerovo fire a "stab in the back" for Putin.
At least one vigil held in memory of the dead in cities across Russian Federation has turned into an anti-government demonstration.
"I mourn together with all the people", said the 28-year old computer expert Alexei Ivanov in St. Petersburg.
One of the trapped girls, Vika Pochankina, called her aunt saying they can't get out and asking to tell her mom that she loved her. "The preliminary suspicion is that a child had a cigarette lighter which ignited foam rubber in this trampoline room, and it erupted like gunpowder", he said.
Another theory, which they say is less likely, is that the blaze began due to someone setting fire to something accidentally or deliberately.
Mr Bastrykin told Mr Putin the mall's fire alarm system had been out of order since 19 March. The shopping center's owner will be questioned and four people, including two employees of the fire alarm system company, have been detained.