President Vladimir Putin announced the move on Tuesday in his annual address to the nation.
The deal, signed in 2010, limits the number of US and Russian nuclear warheads and gives each the power to inspect the other's weapons.
Mr Biden's comments came as he met a key group of Nato allies in Poland.
The group of eastern European states, known as the Bucharest Nine, reiterated their condemnation of Russia's invasion of Ukraine nearly a year since its start.
Putin's decision to suspend involvement in the nuclear treaty was officially pushed through by both houses of Russia's parliament on Wednesday.
But Russia's foreign ministry later said Moscow would continue to comply with the New Start treaty's restrictions in a "responsible approach".
A senior military official told Russia's lower house that the country would continue to observe agreed restrictions on nuclear delivery systems - meaning missiles and strategic bomber planes.
Signed in 2010 by two then presidents - Barack Obama and Dmitry Medvedev - the New Start treaty was designed to prevent nuclear war. It limits the number of strategic nuclear warheads that both sides can deploy, and gives each country the power to inspect the other.
The arrangement came into force in 2011 and was extended 10 years later - although weapons inspections were disrupted by the Covid pandemic.
Each side's limit is 1,550 long-range nuclear warheads, a lower number than under the previous Start deal.
Between them, the two former Cold War rivals account for almost all of the world's nuclear weapons. Russia had previously said it wanted to keep the treaty running - despite hostile rhetoric on both sides during the Ukraine war.
Speaking ahead of the meeting with leaders from the Bucharest Nine nations - which make up Nato's eastern flank - Mr Biden said suspending New Start was a "big mistake" and reiterated the US commitment to the military alliance.
"Article 5 is a sacred commitment the United States has made. We will defend literally every inch of Nato," he said. Article 5 stipulates that an attack on any member state is treated as an attack on all and requires a joint response.
At the meeting he told the assembled leaders that they were the "front line of our collective defence". In a joint statement after the meeting the group said they were committed to increasing Nato's military presence on their territories.
Russia says Nato - which could soon see Sweden and Finland become new members - represents an existential threat.
Mr Putin, speaking at a rally in Moscow to mark a year of the war, said Russia was fighting in Ukraine for its "historical" lands.
"I just heard from the top military leadership of the country that a battle is ongoing right now, for our historical lands, for our people," he said.
Earlier he met China's top diplomat Wang Yi in Moscow and said cooperation with Beijing was "very important to stabilise the international situation".
Mr Wang said Beijing was ready to strengthen its partnership with Moscow and said their relationship would not be affected by pressure from other countries.