Putin on Monday said the investigation under way into the mass shooting had to be conducted "professionally, objectively and without political bias" to determine who was behind the attack.
"The question that arises is who benefits from this?" Putin told a Kremlin meeting to discuss a response to the shooting.
Mukhammadsobir Faizov, a suspect in the shooting at the Crocus City Hall, in court in Moscow. (AP PHOTO)
"This atrocity may be just a link in a whole series of attempts by those who have been at war with our country since 2014 by the hands of the neo-Nazi Kyiv regime.
"We know by whose hand the crime against Russia and its people was committed. But what is of interest to us is who ordered it."
Ukraine denies any involvement in the attack.
Alexander Bastrykin, chairman of the Investigative Committee, Russia's main criminal investigation organ, told the meeting the death toll in Friday's shooting had climbed to 139.
Meanwhile, the gunmen who carried out the attack briefly entered Turkey to renew their Russian residence permits, but their radicalisation did not happen there, a Turkish security official told Reuters on Monday.
There was no existing arrest warrant against the attackers, meaning they could travel freely between Turkey and Russia, said the official, speaking on condition of anonymity, adding that the attackers had been living in Moscow for a long time.
Two of the attackers left Turkey to travel to Moscow on the same flight on March 2, 2024, the person said.
The attack was later claimed by Islamic State.
