In his state of the nation address ahead of the first anniversary of the campaign in Ukraine, Putin also accused the West of escalating the conflict and vowed that Russia would keep fighting to "systematically" achieve its aims.
The Russian leader accused Western powers of wanting "to be done with us once and for all", but said increasingly stringent sanctions on Russia "will not succeed".
Russia's foreign ministry later said in a statement that Moscow would continue to comply with the restrictions on nuclear warheads imposed by the treaty in a "responsible approach".
Hours later, Biden spoke outside Warsaw's Royal Castle during a visit to Poland.
"Ukraine will never be a victory for Russia -- never," Biden said, a day after making a surprise trip to Kyiv for the first time as president.
"There should be no doubt: our support for Ukraine will not waver, NATO will not be divided and we will not tire," he said.
Biden responded directly to Putin's accusations saying the West "is not plotting to attack Russia".
"Millions of Russian citizens who only want to live in peace with their neighbours are not the enemy," he said.
He said Putin "thought autocrats like himself were tough" but faced the "iron will" of the US and its partners.
- 'Irresponsible' -
Russia's decision to suspend its participation in the New START treaty for nuclear disarmament was met with widespread international condemnation.
The 2010 deal is the last remaining arms control treaty between the world's two main nuclear powers but it has frayed in recent years, with the two sides accusing each other of not complying with it.
US Secretary of State Antony Blinken said Russia's decision was "deeply unfortunate and irresponsible" but that Washington was still willing to talk about the issue.
NATO Secretary General Jens Stoltenberg said the move meant that "the whole arms control architecture has been dismantled".
Shortly after Putin's speech, Ukraine's presidential chief of staff Andriy Yermak said on Telegram that Moscow was "strategically at a dead end".
"Our goal is to kick them out of Ukraine and punish them for everything," he said.
Russia said Tuesday it will continue to comply with the nuclear treaty limits despite the suspension.
"Russia intends to adhere to a responsible approach and will continue to strictly comply with the quantitative restrictions on strategic offensive arms stipulated by it (New START) within the life cycle of the treaty," Russia's foreign ministry said in a statement.
- 'Critical moment' -
Biden earlier met with President Andrzej Duda, saying his visit had come "at a critical moment".
He also reaffirmed Washington's "iron-clad" commitment to NATO's principle of collective defence.
Duda said that thanks to Biden "we can see that America can keep the world order".
On Wednesday, Biden is due to meet with the leaders of nine eastern NATO members which have been staunch supporters of Ukraine and where there are fears of the conflict spilling over.
When the Kremlin launched the offensive in Ukraine, its so-called "special military operation" was planned to be a rapid conquest leading to capitulation and the installation of a pro-Russian regime.
Since then, Russia has been forced to give up ground in Ukraine but has kept up a barrage of drone and missile attacks and the military and civilian toll has spiralled.
According to the latest estimates from Norway, the conflict has wounded or killed 180,000 Russian soldiers and 100,000 Ukrainian troops.
Other Western sources estimate the conflict has caused 150,000 casualties on each side.
In Ukraine on Tuesday, President Volodymyr Zelensky blasted Russia for "mercilessly killing" civilians in the southern city of Kherson as local officials reported at least five deaths following strikes there.
AFP reporters saw dead bodies covered with plastic sheets or foil blankets on the streets near a bus stop and a supermarket in Kherson.
Kherson is the capital of one of the four regions -- along with Donetsk, Luhansk and Zaporizhzhia -- that Russia claims to have annexed but has never fully controlled.
- 'Getting out of control' -
On Tuesday, China said it was "deeply concerned" about the conflict, which it said was "intensifying and even getting out of control".
Foreign Minister Qin Gang said Beijing would "urge the countries concerned to stop adding fuel to the fire as soon as possible".
China has sought to position itself as a neutral party, while maintaining close ties with its strategic ally Russia.
China's top diplomat, Wang Yi, is due in Moscow on Tuesday for talks, in his final stop of a European tour. He is expected to meet with Russian Foreign Minister Sergei Lavrov on Wednesday.
Stoltenberg on Tuesday echoed US concerns that China could supply Russia with weapons to help it pursue its campaign in Ukraine.
The Western allies worry they are falling behind in supplying enough shells for Kyiv's artillery to fend off a renewed Russian offensive.
But if the fears -- first raised by Washington -- that China is preparing to deliver weapons to Russia are realised, they could fall even further behind in what would be a growing arms supply race.
Related Links
Learn about nuclear weapons doctrine and defense at SpaceWar.com
Learn about missile defense at SpaceWar.com
All about missiles at SpaceWar.com
Learn about the Superpowers of the 21st Century at SpaceWar.com
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