US President Joe Biden said Russian President Vladimir Putin's threat to use nuclear weapons is the biggest such threat since the Cuban Missile Crisis, as Russia's military leadership faced a rare domestic public backlash over the war in Ukraine.

President Volodymyr Zelensky said Ukraine's forces were swiftly recapturing more territory especially in the south of the country as Putin's seven-month invasion unravels.

Biden said the United States was "trying to figure out" Putin's off-ramp from the war, warning that the Russian leader was "not joking when he talks about potential use of tactical nuclear weapons or biological or chemical weapons, because his military is, you might say, is 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," Biden told Democratic donors in New York on Thursday.

"We have not faced the prospect of Armageddon since Kennedy and the Cuban missile crisis," he said.

In the 1962 crisis, the United States under President John Kennedy and Soviet Union under its leader, Nikita Khrushchev, came close to the use of nuclear weapons over the presence of Soviet missiles in Cuba.

"I don't think there's any such thing as the ability to easily (use) a tactical nuclear weapon and not end up with Armageddon," Biden said.

Biden said he and U.S. officials are searching for a diplomatic off-ramp.

"We're trying to figure out what is Putin’s off-ramp...Where does he find a way out? Where does he find himself in a position he does not, not only lose face but lose significant power in Russia," Biden said.

Biden spoke at the New York home of businessman James Murdoch, turning to the son of conservative media mogul Rupert Murdoch to try to boost his party's chances in Nov. 8 congressional elections.

The event at Murdoch's home was to benefit the Democratic Senatorial Campaign Committee, which is providing support for Democratic candidates for the Senate.