The US President said Russia would “pay a price” for meddling in US elections and suggested Putin has no soul. Asked whether he regarded the Russian leader as a killer he replied “I do”.
The remark sparked fury with Moscow recalling its US ambassador for consultations.
Konstantin Kosachyov, deputy chair of the Russian parliament’s upper house, called on Mr Biden to apologise.
He claimed the US President’s remark “is not allowed from the mouth of a stateman of such a rank”.
Putin responded personally to the comment claiming every country has “bloody events” in its history.
He referenced the US killing of Native Americans, slavery and atomic bomb attacks on Japan during the Second World War.
Asked specifically about the “killer” remark, Putin replied: “I remember in my childhood, when we argued in the courtyard with each other we used to say: ‘It takes one to know one.’
“And that’s not a coincidence, not just a children’s saying or joke.
“The psychological meaning here is very deep.
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Putin also asked Mr Biden to discuss their differences via a video link that would be broadcast live.
He said: “I want to offer President Biden that we continue our discussion, but on the condition that we do it live, online, without any delays.”
On Thursday White House spokesperson Jen Psaki said the President had no regrets about his comments and had no imminent plans to speak with Putin.
She commented: “I would say the President already had a conversation with President Putin, even as there are more world leaders that he has not yet engaged with.
“The President will of course be in Georgia tomorrow and quite busy.”
In August 2020 Russian opposition leader Alexei Navalny was poisoned with the Novichok nerve agent, the same poison used in the 2018 Salisbury attacks.
He survived after being treated in Berlin’s Charite hospital.
Mr Navalny blamed Putin personally for the poisoning and the UK and EU responded with sanctions.
Moscow denies any involvement in both incidents.
Mr Navalny returned to Russia this January and is currently imprisoned in a penal colony.