Russia will observe a national day of mourning on Sunday after a massacre in a Moscow concert hall that killed more than 130 people, the deadliest attack in Europe to have been claimed by the Islamic State (IS) group.

Russian President Vladimir Putin has vowed to punish those behind the "barbaric terrorist attack", saying four gunmen trying to flee to Ukraine had been arrested.

Kyiv has strongly denied any connection, with Ukrainian President Volodymyr Zelensky accusing Putin of trying to shift the blame onto them.

"The whole country is in mourning with those who lost their loved ones in this inhumane tragedy," public television channel Russia 24 said on Sunday morning.

Putin, in his first public remarks on the attack, made no reference to a statement by IS claiming responsibility.

At least 133 people were killed when camouflaged gunmen stormed the Crocus City Hall, in Moscow's northern suburb of Krasnogorsk, and then set fire to the building on Friday evening.

The Islamic State group on Saturday wrote on Telegram that the attack was "carried out by four IS fighters armed with machine guns, a pistol, knives and firebombs," as part of "the raging war" with "countries fighting Islam".

A video lasting about a minute and half apparently shot by the gunmen has been posted on social media accounts typically used by IS, according to the SITE intelligence group.

The video appears to have been shot from the lobby of the concert venue and shows several individuals with blurred faces and garbled voices, firing assault rifles with inert bodies strewn about and a fire starting in the background.

The attack was the deadliest in Russia for almost two decades.

Russian officials expect the death toll to rise further, with more than 150 wounded.

Russia's Investigative Committee, which probes major crimes, said rescue workers were still pulling bodies from the burnt-out building on Saturday.

The emergency situations ministry has so far named 29 of the victims, the blaze having complicated the process of identification.

The ministry on Sunday posted a video of heavy equipment arriving at the scene of the fire to dismantle damaged structures and clear debris.

- 'Barbaric' -

"Terrorists, murderers, non-humans... have only one unenviable fate: retribution and oblivion," Putin said in his televised address on Saturday.

Calling the attack a "barbaric, terrorist act", he said "all four direct perpetrators... all those who shot and killed people, have been found and detained".

Russian television showed security services interrogating four bloodied men, who spoke Russian with an accent, on a road in the western Bryansk region, which borders both Ukraine and Belarus.

"They tried to escape and were travelling towards Ukraine, where, according to preliminary data, a window was prepared for them on the Ukrainian side to cross the state border," said Putin.

Zelensky, in his evening address on Saturday, dismissed the suggestion that Kyiv had been involved.

"What happened yesterday in Moscow is obvious," he said. "Putin and the other scum are just trying to blame it on someone else."

Russia has arrested 11 people in connection with the attack, the FSB security service said. Earlier, the agency had said the attackers had "contacts" in Ukraine, without elaborating.

- Site search to continue -

Putin, whose first public remarks came more than 18 hours after the start of the attack, declared Sunday a day of national mourning.

"All the perpetrators, organisers and those who ordered this crime will be justly and inevitably punished," he promised.

The Investigative Committee said the death toll had so far reached 133 and the governor of the Moscow region said rescuers would continue to scour the site for "several days."

About 107 people were still in hospital, many in a critical condition, Deputy Prime Minister Tatyana Golikova said.

IS had first claimed responsibility for the attack on Friday night, repeating its claim again on Saturday.

Some witnesses filmed the gunmen from the upper floors as they walked through the stalls shooting people, sharing the footage on social media.

Then "the terrorists used a flammable liquid to set fire to the concert hall's premises, where spectators were located, including wounded," the Investigative Committee said.

Investigators said people died from gunshot wounds as well as smoke inhalation after a fire engulfed the 6,000-seater venue.

Investigators said a man who jumped on one of the gunmen as he was shooting at the concert-goers, "immobilising" him and thus "saving the lives of people around him", would receive an award.

- Blood donation queues -

In Washington, a statement from the White House condemning the attack described the IS as a "common terrorist enemy that must be defeated everywhere".

The head of the state-run RT media outlet, Margarita Simonyan, posted two videos of interrogations of two handcuffed suspects. They both admitted to the attack but did not say who had organised it.

The interior ministry said all four of the suspected gunmen were foreign nationals.

Russian Telegram channels -- including those with links to the security services -- said they were from Tajikistan, a country that borders Afghanistan and where the jihadist group is active.

Tajikistan's foreign ministry told Russia's TASS news agency it was in close contact with Moscow over the matter.

In Moscow, residents stood in long queues in the rain to donate blood for those in hospital, and mourners came to lay flowers outside the concert hall.

Memorial posters featuring a single candle replaced some advertising billboards in the capital and major events were cancelled across the country.

Museums, theatres and cinemas announced their closure over the weekend.

- US warning dismissed -

Just three days earlier, Putin had publicly dismissed a US warning of an "imminent" attack in Moscow as propaganda designed to scare Russian citizens.

The US embassy in Russia had warned on March 7 that "extremists have imminent plans to target large gatherings in Moscow, to include concerts", advising caution over the following 48 hours.

Washington said after the attack it had also shared details directly with Moscow.

But speaking to FSB chiefs last Tuesday, Putin had called it a "provocative" statement and "outright blackmail... to intimidate and destabilise our society".