Thousands of Kemerovo city residents have held a protest in Russia's Siberia, demanding the resignation of local officials after a deadly shopping centre fire.

Protesters gathered at Kemerovo's Sovetov Square on Tuesday, saying that they do not believe the official version of events on the fire that started in the Winter Cherry mall, Russia's Interfax news agency reported.

The official death toll stood at 64, but protesters said they believed the number was higher. They also said the number of the rescue workers was exaggerated.

Chanting slogans, such as "the truth", protesters at the demonstration demanded the resignation of Aman Tuleev, the governor of Kemerovo district, Interfax reported.

Sergey Tsyvilev, the deputy governor of Kemerovo district, came to meet the demonstrators and addressed them with a loudspeaker.

"You can hear me; you can look me in the face. I am responsible for my words," he said before he was interrupted by the protesters with calls for his resignation, a video posted by Interfax showed.

"The official list [of the dead] is put out at local schools," he said. The protesters shouted back, asking why it was not published in local media instead.

When he mentioned the official number of 64 dead, the demonstrators started to whistle and boo at him.

"It's a lie, it's a lie," shouted the protester closest to him. "Why do you lie?"

Some of the protesters brought framed pictures of their dead or missing loved ones. Others carried posters that read: "Who is to blame?"

The authorities mobilised security forces at the protest site. At least eight buses, six minibuses, about 10 cars carrying special forces and five ambulances came to the square, Interfax reported, forming a wall of defence in front of the city's administration building.

Meanwhile, locals kept bringing flowers and toys to a makeshift memorial near the burnt-down shopping centre, a witness told Interfax, saying a number of taxi drivers brought people to the memorial for free.

Vladimir Puchkov, Russia's minister of emergency situations, told reporters in Kemerovo on Tuesday that rumours circulating on social media about hundreds of dead were not true.

"A total of 64 bodies have been found so far. The search for the rest of people continues," he said.

A group of volunteers has since issued an alternative list of missing people, Interfax reported.

One of the volunteers told the news agency that there were already 78 missing persons on the group's list, including 70 children.

Also on Tuesday, Russia's President Vladimir Putin visited Kemerovo, laying flowers at the memorial.

He later told off the mayor of the city for failing to make sure the fire safety measures were in place at the shopping centre.

Putin visited several injured people in a hospital and spoke separately to a group of protesters who doubted the official casualty numbers.

He told them that there was no point in doubting the official death toll and assured them that "all of those who are to blame will be punished".

Later the city's mayor took the group to the morgue to count the dead.