Mr Biden said Russia’s President Vladimir Putin was “not joking” when he spoke of using tactical nuclear weapons after suffering setbacks in Ukraine.
The US was “trying to figure out” Mr Putin’s way out of the war, he added.
The US and the EU have previously said Mr Putin’s nuclear sabre-rattling should be taken seriously.
However, the US National Security Adviser Jake Sullivan last week said that despite Moscow’s nuclear hints, the US had seen no signs that Russia was imminently preparing to use a nuclear weapon.
Speaking at a private fundraising event, President Biden said the Russian leader was “not joking” when he talked about using tactical nuclear, biological or chemical weapons – “because his military is, you might say, significantly underperforming”.
“For the first time since the Cuban Missile Crisis, we have a direct threat to the use of nuclear weapons, if in fact things continue down the path they’d been going,” Mr Biden told fellow Democrats.
“We have not faced the prospect of Armageddon since Kennedy and the Cuban missile crisis.”
In 1962, the US and the Soviet Union – under President Kennedy and Nikita Khrushchev – came close to a nuclear showdown over the deployment of Russian nuclear weapons in Cuba.
The confrontation is considered by many experts to be the closest the world has ever come to a full-scale nuclear war.