In a televised address, Putin said all four gunmen had been arrested before they had a chance to cross the border into Ukraine.
“I am speaking to you today in connection with the bloody, barbaric terrorist act, the victims of which were dozens of innocent, peaceful people,” Putin said in his first public remarks since the attack.
“Terrorists, murderers, non-humans will face the unenviable fate of retribution and oblivion,” said Putin, who declared Sunday a day of national mourning across Russia.
The FSB security service said the gunmen had contacts in Ukraine and were captured near the border. It said they were being transferred to Moscow.
Ukrainian military intelligence spokesman Andriy Yusov said: “Ukraine was of course not involved in this terror attack. Ukraine is defending its sovereignty from Russian invaders, liberating its own territory and is fighting with the occupiers’ army and military targets, not civilians.”
He said the FSB version that the suspects were arrested en route to Ukraine was “of course another lie from the Russian special services”.
A senior Russian lawmaker, Andrei Kartapolov, said that if Ukraine was involved, then Russia must deliver a “worthy, clear and concrete” reply on the battlefield.
The death toll was the biggest single loss of life from terrorism in Moscow since Chechen separatists took hostages in 2002 at the Nord-Ost theatre. At least 170 people including the dozens of attackers died during a botched rescue mission.
At a meeting with senior FSB officers on Tuesday, Putin hit out at “frankly, provocative statements” by Western officials this month warning of a possible imminent terrorist attack. “All this resembles outright blackmail and the intention to intimidate and destabilise our society,” the president said.
Moscow attack: more than 1 Isis branch involved, Russia in its ‘crosshairs’
Moscow attack: more than 1 Isis branch involved, Russia in its ‘crosshairs’
The US Embassy in Moscow issued a public warning on its website on March 7 that “extremists have imminent plans to target large gatherings in Moscow, to include concerts.”
“The US government also shared this information with Russian authorities in accordance with its long-standing ‘duty to warn’ policy,” she added.
The FSB said earlier this month it had prevented an attack on a Moscow synagogue by what it called an Afghan branch of Islamic State, Interfax reported.