Mr Biden said the US was “trying to figure out” what Mr Putin's exit strategy from the war could be, as Ukraine continues to recapture territory.
“For the first time since the Cuban Missile Crisis, we have the threat of a nuclear weapon if in fact things continue down the path they are going,” Mr Biden said late on Thursday at a donor event in New York.
“We have not faced the prospect of Armageddon since [President John F] Kennedy and the Cuban Missile Crisis.”
The White House said the warning from Mr Biden was not tied to new intelligence reports.
Press Secretary Karine Jean-Pierre told reporters on Friday that Washington has not seen new indications that Mr Putin has decided to use a nuclear weapon against Ukraine.
“We have not seen any reason to adjust our own strategic nuclear posture nor do we have [any] indication that Russia is preparing to imminently use nuclear weapons,” she said on Air Force One.
Concern has been mounting over Russia possibly deploying a “tactical” nuclear weapon, which is designed for use on the battleground, as opposed to a long-range “strategic” nuclear weapon.
The Russian president is “not joking when he talks about potential use of tactical nuclear weapons or biological or chemical weapons because his military is, you might say, significantly underperforming,” Mr Biden said.
He said there was no scenario in which one uses a nuclear weapon and does “not end up with Armageddon”.
Ukrainian President Volodymyr Zelenskyy said his forces were recapturing vast areas of land from Russian forces as Moscow continued to experience losses seven months into its invasion.
Mr Zelenskyy announced in a televised addressed that Kyiv forces had recaptured more than 500 square kilometres and dozens of settlements in Kherson since Mr Putin announced Russia had annexed four Ukrainian regions.
The Russian president has responded by mobilising hundreds of thousands of men to the front line.
Now, the White House is trying to understand what the end game for Mr Putin could be.
“Where does he find a way out?” Mr Biden said. “Where does he find himself where he does not only lose face but significant power?”