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Russia’s FSB security service has arrested 11 people it said were responsible for an attack at a Moscow rock concert that killed at least 133 people.

The four men directly involved in the shooting were among the group detained, the FSB said on Saturday.

Isis has claimed responsibility for the attack, according to news agency reports, and the White House called the group a “common terrorist enemy that must be defeated everywhere” in a statement condemning the killings.

But Russian president Vladimir Putin hinted at Ukrainian involvement. In a televised address on Saturday Putin condemned the attack as a “bloody, barbaric terrorist act” but made no mention of Isis.

The four assailants “were trying to flee and were heading towards Ukraine”, Putin said, claiming that “according to preliminary information, a window for crossing the state border had been prepared for them on the Ukrainian side”.

Ukrainian president Volodymyr Zelenskyy denied any involvement in the attacks, saying the accusation was a ploy by Putin to justify escalating his war.

“They have brought hundreds of thousands of their terrorists here, to Ukrainian land, they fight against us, and they don’t care what’s happening inside their own country,” he said on Saturday night.

FSB officials said they had detained the gunmen in the Bryansk region, which borders Ukraine. Dashcam footage from a nearby vehicle had caught them arriving at the scene in a white Renault car before the attack took place.

The FSB claimed the men were trying to flee from Russia to Ukraine, and said they had “relevant contacts” there. Kyiv has completely denied any involvement in the attack.

Baza, an anonymous channel on the Telegram messaging app which is close to the Russian police, said the assailants were from Tajikistan, a Central Asian country that has witnessed Isis activity in the past. Its foreign ministry denied the reports.

Videos also circulated on Telegram of Russian security services detaining several men from Tajikistan, dragging one man bleeding through some woodland, and interrogating another man kneeling by the roadside in the Bryansk region.

Putin pledged that Moscow would find and punish everyone involved in the attack, “whomever they may be, and whoever sent them”.

“We will identify and punish everyone who stands behind the terrorists, who prepared this evil act, this attack on Russia,” he said.

The Russian Investigative Committee said on Saturday the death toll was expected to climb.

Moscow region governor Andrey Vorobyev, who visited the scene of the attack, said “the situation there is extremely bad” and “the number of victims will rise significantly”.

Many people were shot and killed by the gunmen who were dressed in camouflage as they stormed through the building, while others died in a blaze that tore through the venue after the attackers set off explosions in the hall.

Images shared by emergency services showed firefighters removing charred seating in the main auditorium, where people had hidden between chairs as the shooting began.

The assault has shocked Russia, triggering an outpouring of grief, with memorials for victims springing up across the country. It is the largest loss of life in a terrorist attack in Russia in at least a decade, and recalls the Islamist insurgencies that marked the first decade of Putin’s rule.

It will also remind Moscow residents of the Nord-Ost siege, when Chechen fighters took hundreds of people hostage in a Moscow theatre in 2002, leading to the deaths of more than 170 people.

The US embassy in Moscow and six other western countries’ missions issued alerts in early March warning about attacks on public venues, including concerts.

Moscow mayor Sergey Sobyanin has cancelled all big public events in the capital planned for the weekend. Several other Russian cities have followed suit.