"All four perpetrators, who were directly involved in the terrorist attack, all those who shot and killed people, have been found and apprehended," Putin was quoted as saying by Sputnik in his national address.

"They attempted to escape and were heading towards Ukraine, where, according to preliminary information, a window was prepared for them on the Ukrainian side to cross the state border," he said.

The President, who was recently reelected to power for another term, confirmed 11 people have been arrested in total so far.

He said: "The investigative and law enforcement agencies will spare no effort to establish all the details of this crime."

Despite mentioning 'terrorists', Putin did not refer to Islamic State group in his speech which claimed responsibility for the attack.

At least 133 people were killed after gunmen stormed into a concert hall close to Moscow and opened fire on people attending an event.

Top world leaders, including Indian PM Narendra Modi, condoled the deaths in the incident.

US denies Ukraine involvement

White House spokesman John Kirby denied Ukraine's involvement in the attack.

He said: "There is no indication at this time that Ukraine or Ukrainians were involved in the shooting. But, again, this just broke. We’re taking a look at it. But I would disabuse you at this early hour of any connection to Ukraine."

Ukraine's Ministry of Foreign Affairs denies Russian charges

Ukraine's Ministry of Foreign Affairs has rejected all accusations leveled aginst the country by Russia over its possible involvement in the attack.

"We consider such accusations to be a planned provocation by the Kremlin to further fuel anti-Ukrainian hysteria in Russian society, create conditions for increased mobilisation of Russian citizens to participate in the criminal aggression against our country and discredit Ukraine in the eyes of the international community," the Ministry said in a statement.

"There are no red lines for Putin's dictatorship. It is ready to kill its own citizens for political purposes, just as it has killed thousands of Ukrainian civilians during the war against Ukraine as a result of missile attacks, artillery shelling and torture," it said.

More than 6,000 concertgoers were present inside hall

Over 6,000 concertgoers were present in the hall when they were attacked by gunmen.

The attack took place ahead of a concert by Russian rock group Picnic.

The band members remained unharmed.

A security guard described how the heavily-armed attackers stormed into the hall and started firing bullets as he and his colleagues were working at the central entrance.

"There were three other security guards and they hid behind an advertising board," he told Russian telegram channel Baza as quoted by BBC "And those attackers passed 10m [30ft] away from us - they started shooting randomly at people on the ground floor."

Attack after Putin returns to power

The attack took place just days after Putin returned to power as Russian President after winning the presidential election with no major opponents fighting against him.

Several Western nations had denounced the elections as neither free nor fair.