The Kremlin said Monday it would not comment on Islamic State's claims of responsibility for the  Moscow concert hall massacre as the investigation was under way.

"The investigation is ongoing. No coherent version has been voiced yet. We are talking only about preliminary data," Kremlin spokesman Dmitry Peskov told reporters, adding that President Vladimir Putin had no plans to visit the site of the attack.

On Sunday Russia ordered four men accused of killing at least 137 people in the concert hall massacre to be held in custody on "terror" charges with the death toll expected to climb as more than 100 people are hospitalised.

The men face life in prison, although Russian officials have clamoured for the lifting of a moratorium on the death penalty to deliver even harsher sentences. 

In a series of late-night court hearings in Moscow that ran into the early hours of Monday, the four men -- with bruises and cuts over their faces -- were dragged into the court in front of dozens of reporters who had assembled at the capital's Basmanny district court. 

FSB security service officers wheeled one into the hearing on a medical gurney, following reports and videos on Russian social media of bloody interrogations after the men were arrested on Saturday.

In his only public remarks since, President Vladimir Putin pointed to a Ukrainian connection, saying the four suspects gunmen were arrested while trying to flee there.

- 'Terrorists have no nationality' -

Gunmen in camouflage stormed the Crocus City Hall concert venue on Friday night, shooting concert-goers before setting the building ablaze and fleeing the scene, Russian investigators say.

More than 5,000 people were in the building, Russian state media cited a spokesperson from the venue owner as saying Monday.

It was the deadliest attack in Russia in two decades and the most fatal in Europe to have been claimed by IS.

The Moscow court ordered the men to be held in pre-trial detention until May 22 -- a date that is likely to be extended until a full trial.

Russia said Saturday it had arrested 11 people in connection with the attack. There has been no information on the other seven.

The four suspected shooters were all citizens of Tajikistan, Russian state media reported.

The president of Tajikistan -- a Central Asian nation that borders Afghanistan and where IS is known to be active -- told Putin in a phone call on Sunday: "Terrorists have no nationality."

Moscow and Dushanbe agreed to "intensify" their counter-terrorism co-operation, the Kremlin said in a readout of the call.

The court said two of the defendants had pleaded guilty.

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, and the United States has said IS bears "sole responsibility".

Health officials said Sunday evening the number of those injured stood at 182, with 101 people still in hospital, of whom 40 were in "critical" or "extremely critical" condition. 

- 'Machine guns, knives, firebombs' -

The Islamic State group said 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 theatre shooting spectators, the gunmen set fire to the building, trapping many inside.

They said victims died from gunshot wounds and smoke inhalation.

Russia observed a day of national mourning on Sunday, as dozens came to lay flowers at the burnt-out concert hall in Moscow's northern Krasnogorsk suburb.

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

Museums, theatres and cinemas around the country closed and billboards and advertising screens were replaced with memorial messages.

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

- 'Barbaric terrorist attack' -

Abroad, people left floral tributes outside Russian embassies.

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

Critics of the Kremlin have questioned why Russia's powerful security agencies were unable to foil the attack, despite public and private warnings from Western intelligence services just two weeks earlier.

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".