He also accused Ukraine of preparing a “window” to help the suspects escape even as Kyiv has denied any role in the attack.
Putin made these known in a public address he delivered on Saturday in Moscow, Russia’s capital.
Earlier, on Friday, gunmen in camouflage clothing opened fire on people at a concert in the Crocus City Hall near Moscow.
Several Russian media outlets reported that automatic weapons were used in what many have termed ‘one of the worst such attacks in Russia in years.’
Reuters had earlier reported that least five gunmen were shown in unverified videos firing repeatedly at screaming civilians cowering in the concert hall as Soviet-era rock group “Picnic” was about to perform.
Putin, in a five-minute televised address, claimed that someone in Ukraine had tried to help the attackers escape across the border from Russia before they were apprehended by Russian security services.
He did not definitively pin the attack on Ukraine, nor did he refer to the assessment by American officials that a branch of the Islamic State was behind it.
However, he pledged to punish the perpetrators, “whoever they may be, whoever may have sent them.”
Meanwhile, Russia has arrested 11 people, including all four gunmen suspected of carrying out the attack, the head of the country’s Federal Security Service stated in a statement.
The Russian Investigative Committee said at least 133 people are now known to have been killed as more bodies were found in the rubble.