"It's obvious that Putin and other thugs are just trying to blame someone else," Zelenskiy said in his nightly video address on Saturday.

"Their methods are always the same. We've seen it all before, destroyed buildings and shootings and explosions. And they always find someone else to blame."

Chechen rebels accused Russian secret services of being behind apartment bombings in Moscow, Buynkask and Volgodonsk, blamed on Chechens, that killed more than 200 people in Russia in 1999, prompting Putin, who was then prime minister, to send troops back to Chechnya.

A Russian foreign ministry spokeswoman said Zelenskiy was "the only head of state crazy enough to blame Russia for the terrorist attack".

Earlier, Putin said 11 people had been detained following the attack, including the four gunmen.

"They tried to hide and moved towards Ukraine, where, according to preliminary data, a window was prepared for them on the Ukrainian side to cross the state border," Putin said.

Militant Islamist group Islamic State claimed responsibility for Friday's rampage at Crocus City Hall, which Russian authorities say killed at least 133 people.

Zelenskiy said Putin should use his own men to fight terrorism at home instead of invading Ukraine.

"They have brought hundreds of thousands of their own terrorists here, on Ukrainian land, to fight against us, and they don't care about what is happening inside their own country," he said.

"Yesterday, as all this happened, instead of dealing with his fellow Russian citizens, addressing them, the wimp Putin was silent for a full 24 hours, thinking about how to tie this to Ukraine. It's all absolutely predictable."

Australian Associated Press