According to the statement of the Kemerovo administration, Aman Tuleyev submits resignation as governor of the Russian Kemerovo region on a voluntary basis, according Sputnik.
There were protests as Tuleyev himself was criticised for failing to visit the scene of the tragedy in the first few days after the incident.
"Since March 25, the Kemerovo Region administration has received 811 petitions from citizens".
Tuleyev, who had been at the helm of the key coal-mining region since 1997, said he could no longer remain at his post with "such a heavy burden" and added that his resignation was "the only right choice".
"Putin called Tuleyev over the phone and thanked him for many years of his work in the post of the region's head", the spokesman said.
Officials put the death toll at 64 people, including at least 41 children, and said 25 of the 76 injured were hospitalized.
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Chanting slogans such as "the truth", protesters at Tuesday's demonstration demanded the resignation of Tuleev.
Meanwhile, the majority of Russians blame owners and managing staff of the shopping compound for the deadly blaze in the Siberian city of Kemerovo, a survey made by Russian Public Opinion Research Center (VTsIOM) said on Friday.
Some parents lost all their children, and the youngest victim was a two-year-old toddler.
Among other things, officials said fire exits were illegally blocked, the fire alarm system was out of order and children had been locked inside cinemas. Tuleyev also told Putin that "troublemakers" and "opposition forces" were attempting to stoke unrest for political gain.
Critics say that, while Putin has taken numerous steps to strengthen the Kremlin's grip on Russian Federation, he has been unable to establish the kind of control that could curb the graft and negligence that can lead to accidents or increase their human toll.