Ukrainian President Volodymyr Zelensky on Saturday accused Russia's Vladimir Putin of seeking to "shift the blame" onto Kyiv for the Moscow concert hall attack that killed 133 people.

"What happened yesterday in Moscow is obvious: Putin and the other scum are just trying to blame it on someone else," Zelensky announced, after Putin said the suspects had been fleeing towards Ukraine.

"They always have the same methods," Zelensky added.

In a televised address earlier Saturday, President Putin said the four gunmen arrested for the deadly attack were "travelling towards Ukraine, where, according to preliminary data, a window was prepared for them on the Ukrainian side to cross the state border".

Kyiv has angrily dismissed the claims by the Russian leader, which come more than two years after Moscow invaded Ukraine.

"That low-life Putin, instead of dealing with his Russian citizens, addressing them, was silent for a day, thinking about how to bring it to Ukraine," Zelensky said.

"Everything is absolutely predictable."

The Moscow attack has been claimed by the Islamic State group (IS). 

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

Putin made no reference to the group's claims of responsibility in his address.