Speaking at the UN General Assembly in New York, Biden said: "A permanent member of the United Nations Security Council invaded its neighbor, attempted to erase a sovereign state from the map."
He added: "Russia has shamelessly violated the core tenets of the United Nations Charter."
He slammed Russian President Vladimir Putin for making "reckless" and "irresponsible" threats to use nuclear weapons.
Earlier in the day, Putin ordered a partial mobilization of 300,000 reservists to fight in Ukraine and warned the West he was ready to use nuclear weapons to defend Russia.
"Again, just today, President Putin has made overt nuclear threats against Europe, in a reckless disregard for the responsibilities of the nonproliferation regime," Biden told world leaders at the UN.
"A nuclear war cannot be won and must never be fought," he cautioned.
"Putin claims he had to act because Russia was threatened, but no one threatened Russia and no one other than Russia sought conflict," Biden also said in his speech.
He added: "This war is about extinguishing Ukraine's right to exist as a state, plain and simple, and Ukraine's right to exist as a people. Wherever you are, wherever you live, whatever you believe, that should ... make your blood run cold."
"We will stand in solidarity against Russia's aggression, period," he vowed.
Wednesday was day 210 of Russia's war in Ukraine.
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Source: IAR, PAP, CNN, Reuters