The US president says Russia has "shamelessly violated the core tenets" of the United Nations charter with its "brutal, needless war" in Ukraine.
Delivering a forceful condemnation of Russia's invasion to the international body, Joe Biden said reports of abuses against civilians in Ukraine "should make your blood run cold".
He also said President Vladimir Putin's new nuclear threats against Europe showed "reckless disregard" for his nation's responsibilities as a signatory of the Treaty on the Non-Proliferation of Nuclear Weapons.
"A nuclear war cannot be won and must never be fought," he added.
"We will stand in solidarity against Russia's aggression. Period."
Mr Biden said no one had threatened Russia, despite its claims to the contrary, and that only Russia had sought conflict.
And he criticised Russia for scheduling "sham referenda" this week in territory it has forcibly seized in Ukraine.
Earlier, Mr Putin ordered a "partial mobilisation" of military reserves - a move that Russia's defence minister said amounted to around 300,000 troops.
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It means people with previous military experience will join the war unless they are too old or medically unfit.
He cited claims of Ukraine shelling the Russian-occupied Zaporizhzhia nuclear power plant and said some representatives of NATO states had raised the possibility of using nuclear weapons against Russia.
He warned them his country "has various weapons of destruction, and with regard to certain components they're even more modern than NATO ones".
He also approved referendums in four Ukrainian regions under Russian occupation.
Donetsk, Luhansk, Kherson and Zaporizhzhia announced the plans on Tuesday.
They are scheduled to take place from 23 to 27 September. Together, the regions make up about 15% of Ukrainian territory.