Bortnikov made the statement at a meeting of the Council of Heads of Security Agencies and Special Services of the Commonwealth of Independent States in Bishkek, Kyrgyzstan.
He said: "The investigation is ongoing, but it is already safe to say that Ukrainian military intelligence has a direct connection to this attack."
Bortnikov promised that "all circumstances of the crime will be established and everyone involved in it will not escape punishment."
A shooting at Moscow's Crocus City Hall concert venue on March 22, followed by a massive fire, resulted in at least 144 deaths and 551 injuries, according to official statistics.