Police and ambulances are seen at the scene of a shooting at School No. 175 in Kazan, Tatarstan, on Tuesday. AFP

At least seven school children and one teacher were killed on Tuesday and many more wounded after a lone teenage gunman opened fire in a school in the Russian city of Kazan, the mayor's office said, prompting a Kremlin call for tighter gun controls.

Two children could be seen leaping from the third floor of the four-storey School Number 175 to escape as gunshots rang out, in a video filmed by an onlooker that was circulated by Russia's RIA news agency.

Calling the attack a big tragedy for the whole country, Rustam Minnikhanov, the head of the wider Tatarstan region, said there was no evidence that anyone else had been involved.

"We have lost seven children...four boys and three girls. And 16 people, 12 children and four adults, are in hospital," Minnikhanov told state TV.

"The terrorist has been arrested. He's a 19-year-old who was officially registered as a gun owner."

It was possible the toll would still rise.

Six children were in grave condition in hospital, RIA said. Earlier, Russian news agencies, citing a health ministry source, said 11 people had died.

Footage posted on social media showed a young man being pinned to the ground outside the school building by a police officer.

A woman cries as she is taken to an ambulance at the scene of a shooting at School No.175 in Kazan on Tuesday. AFP

An unconfirmed social media account belonging to the alleged shooter, which was later blocked, contained posts in which he described himself as a bloodthirsty deity and said he planned to kill a "huge number" of people before shooting himself.

President Vladimir Putin ordered the head of the national guard to draw up tighter gun regulations, the Kremlin said.

The alleged gunman was issued a permit for a Hatsan Escort PS shotgun on April 28, Alexander Khinshtein, a lawmaker in the lower house of parliament, wrote on social media.

Kazan is the capital of the Muslim-majority region of Tatarstan and located around 725 km east of Moscow.

The incident was Russia's deadliest school shooting since 2018 when a student at a college in Russian-annexed Crimea killed 20 people before turning his gun on himself.

Reuters