The Russian annexation, though expected, escalated an already heated conflict that's become fraught with potential nuclear implications.
Biden said his administration would support any effort by Ukraine to retake the annexed territories by force, setting the stage for further hostilities.
"America and its allies are not going to be intimidated by Putin and his reckless words and threats," Biden told reporters on Friday, adding Putin "can't seize his neighbour's territory and get away with it".
Russian President Vladimir Putin's announcement that Russia is incorporating four Ukrainian cities and areas was not unexpected following referendums this week that the West had denounced as shams.
But the developments dramatically increased tensions to a point not seen since the Cuban Missile Crisis 60 years ago during the Cold War.
Biden had spoken out against the annexation plans last week at the UN General Assembly, where a vast majority of other members also voiced support for respecting the territorial integrity of all nations.
On Friday, he reiterated the US and NATO allies would not allow Russia to attack any nearby NATO members without facing a strong military response.
"America is fully prepared, prepared with our NATO allies to defend every single inch of NATO territory. Every single inch," Biden said.
"And so, Mr Putin, don't misunderstand what I'm saying. Every inch."
Meanwhile, the US and its European allies are rushing to complete agreement on a measure they hope will do more to damage Russia's economy: a cap on Russia's maritime oil exports that would undermine the prices Putin can demand for his country's oil globally.
For now, Biden said the new US financial penalties, similar to those coming from like-minded countries, will impose severe costs on people and companies "that provide political or economic support to illegal attempts to change the status of Ukrainian territory".
The sanctions will apply to countries, people or firms that support or do business with Russia-backed authorities in the newly annexed areas.
Secretary of State Antony Blinken, echoing Biden, said the US "unequivocally rejects Russia's fraudulent attempt to change Ukraine's internationally recognised borders ... This is a clear violation of international law and the United Nations Charter."
Blinken also spoke out against Putin's nuclear threats, but said the US had not seen anything to suggest the use of nuclear weapons was imminent.
"This kind of loose talk about nuclear weapons is the height of irresponsibility, and it's something that we take very seriously," he said.
The Biden administration did not embrace Ukrainian President Volodymyr Zelenskiy's push on Friday for an accelerated path to NATO membership. Sullivan said the US was focused on supporting Ukraine through "practical, on-the-ground support".
