Minnikhanov's office later added that a teacher was also killed.
Local officials noted that some of the children were evacuated from the school, while others still remained in the building.
Tatarstan President Rustam Minnikhanov had arrived at the scene, agencies reported.
At least 11, including students and a teacher, have died and many more wounded after two unidentified gunmen opened fire at a school in Russia's Kazan on Tuesday morning.
Footage of the school building showed dozens of ambulances lined up in front of the entrance.
"I was in class, I first heard an explosion, then gunshots", TASS quoted a teacher as saying.
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Jonathan McDowell, of the Harvard-Smithsonian Center for Astrophysics, told Fox News on Friday. It was reported to have damaged several buildings, though no injuries were recorded.
The shooting took place in Kazan, roughly 700km east of Moscow.
While school shootings are relatively rare in Russian Federation, there have been several violent attacks on schools in recent years, mostly carried out by students.
At least 20 people have been injured, RIA Novosti reported.
"The terrorist has been arrested, [he is] 19 years old".
Russian President Vladimir Putin at the time blamed the attack on "globalisation" and online communities dedicated to American school shootings which promoted "fake heroes".
The Crimea shooter, Vladislav Roslyakov, was able to legally obtain a gun licence after undergoing marksmanship training and being examined by a psychiatrist.
A teenager was detained after the attack at the school, located some 820km (510 miles) east of Moscow in the mainly Muslim republic of Tatarstan.
The shooting led to calls for tighter gun control in Russian Federation.