Four men accused of involvement in a massacre at a Moscow concert hall that killed 137 people were remanded in custody Sunday, as Russia observed a national day of mourning following the attack claimed by the Islamic State. All four suspects have been charged with terrorism, according to Moscow's Basmanny district court, and face life imprisonment. Their detention is set until May 22 but may be extended depending on the date of their trial.

The court said two of the defendants had pleaded guilty, and one of them, from Tajikistan, had "entirely acknowledged his guilt."

President Vladimir Putin has vowed to punish those behind the "barbaric terrorist attack," and on Saturday said the four gunmen had been arrested while trying to flee to Ukraine. Kyiv has strongly denied any connection to the attack.

Putin has made no public reference to the Islamic State group's claims of responsibility.

At least 137 people, including three children, were killed Friday evening when gunmen stormed the Crocus City Hall in Moscow's northern suburb of Krasnogorsk then set fire to the building.

It is the deadliest attack in Europe to have been claimed by IS.

Russia's Investigative Committee posted a video of the four suspects being dragged into its headquarters in Moscow.

There was no statement on the other seven suspects arrested in connection with the attack.

Officials have said the gunmen were all foreign nationals.

The Islamic State group posted Saturday 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 filmed by the gunmen, has been posted on social media accounts typically used by IS, according to the SITE intelligence group.

The video -- which appears to have been filmed from the lobby of the concert venue -- shows several individuals with blurred faces and garbled voices, firing assault rifles with inert bodies strewn on the floor and a fire starting in the background. Russian investigators said that after walking through the theater shooting spectators, the gunmen set fire to the building, trapping many inside.

Health officials said the number of casualties had risen to 182, with 101 people still in hospital, of whom 40 were in "critical" or "extremely critical" condition. The attack was the deadliest in Russia since the Beslan school siege in 2004.

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

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

On the streets of the capital Sunday, there was shock and grief.

"It is a tragedy. I was morally crushed," Ruslana Baranovskaya, 35, told Agence France-Presse.

"People don't smile ... everybody feels the loss," said 73-year-old Valentina Karenina, a pensioner standing on a street off Red Square.

Museums, theaters and cinemas around the country closed and billboards were replaced with memorial posters.

Mourners continued to stream to the concert hall in northwest Moscow to lay flowers as a tribute to the victims.

More than 5,000 people donated blood following the attack, officials said, with many standing in long queues outside clinics.

Abroad, people left floral tributes outside Russian embassies in sympathy.

Putin on Saturday vowed "retribution and oblivion" to the "terrorists, murderers and non-humans" who carried out the "barbaric terrorist attack."

Several of his allies have called for the country to lift a moratorium on the death penalty, sparking concern among Kremlin critics.

Putin's statement Saturday suggested a Ukraine connection.

"They tried to escape and were traveling towards Ukraine, where, according to preliminary data, a window was prepared for them on the Ukrainian side to cross the state border," Putin said of the attackers in his televised address.

Ukrainian President Volodymyr Zelenskyy, in his own evening address Saturday, rejected any suggestion that Kyiv had been involved. In Moscow, some also doubted Putin's claims.

"I'm not inclined to believe the version about Ukraine's involvement ... this is more like those committed by Islamist extremists," said Vomik Aliyev, a 22-year-old who often went to the concert hall and who said his parents were Muslim.

Washington also dismissed any suggestion that Kyiv had been involved.

"ISIS bears sole responsibility for this attack," said White House National Security Council spokesperson Adrienne Watson.

Late on Sunday, French Prime Minister Gabriel Attal announced the country was returning to its top security alert status in the wake of the attack and given "the threats weighing on our country."

He attributed the attack to the Islamic State group. (AFP)