Twelve more children and four adults were hospitalised in the attack, Minnikhanov said.
At least nine people, mostly children, have died in a shooting at a school in Russian Federation, state media are reporting.
It said eight students and one teacher had been killed and that police had sealed off the fourth floor of the school and were attempting to detain the second attacker.
According to the Interfax news agency, two gunmen opened fire in the school, and one of them - a 17-year-old - has already been apprehended.
Videos posted on social media appeared to show people jumping out of windows to apparently escape the shooting.
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The city administration was cited as saying that children were evacuated from the school and that security had been bolstered at other educational facilities in the city.
School shootings are rare in Russian Federation.
In October 2018, a teenage gunman killed 20 people at the Kerch technical college in Crimea, the peninsula Russian Federation annexed from Ukraine in 2014.
Eyewitnesses had reported an explosion at the school ahead of the shooting.
He was shown in camera footage wearing a similar T-shirt to Eric Harris, one of the killers in the 1999 Columbine High School shooting in the USA, which left 13 people dead. According to authorities, the second shooter is a 19-year-old individual, who had an officially registered gun.