WASHINGTON — Russia’s decision to order troops into Ukraine on Monday presented the United States and Europe with the challenge of deciding how quickly to move in imposing stiff sanctions on Moscow, seeking to balance punishment, deterrence and maintaining unity among the allies.

President Biden’s initial reaction was cautious, limited to issuing a narrow set of sanctions aimed at two regions in eastern Ukraine that are partly controlled by Russian-backed separatists and that President Vladimir V. Putin of Russia recognized as independent on Monday.

The targeted nature of the penalties appeared intended to allow the United States and its European allies to hold in reserve the most aggressive sanctions they have threatened to impose on Moscow if Mr. Putin carries out a full-scale assault to bring down Ukraine’s democratically elected government.

In private, administration officials have conceded that Mr. Putin did not seem interested in further negotiations that did not address his core demands that NATO stop expanding to the east, and speculated that he had tolerated diplomatic overtures mostly to gain time to mass his forces.

White House officials said a further Western response was almost certain to be announced on Tuesday, by which time several of Mr. Biden’s aides said they expected to see Russian forces rolling over the border into Ukraine, crossing the line that Mr. Biden had set for imposing “swift and severe” sanctions on Moscow.

The harshest of those include cutting Russia’s largest banks off from the global economic system, starving Russian heavy industry of semiconductors and other advanced technology, and — if it comes to it — arming an insurgency as Ukrainians fight for their freedom.

But it was not clear that Mr. Biden or his more reluctant allies — especially Germany and Italy, which are dependent on Russian gas imports — were ready to unleash the full sanctions package.

Mr. Putin’s incremental approach to ratcheting up the pressure on Ukraine appears intended to exploit any fissures in what has been a quite unified NATO and European posture. Some nations may be reluctant to reach for the most punishing sanctions if Mr. Putin’s forces remain in Russian-speaking eastern Ukraine, where Russia has exercised great influence during an eight-year conflict.

Yet the limited geographic reach of Mr. Putin’s initial claim on Ukrainian territory stood in sharp contrast to the implication in his winding, hourlong speech on Monday that the entire country was a part of Russia.

He made clear his wider ambition was to reclaim Ukraine and continue rebuilding the empire that collapsed with the end of the Soviet Union three decades ago. At one point he said it outright: “Modern-day Ukraine was in full and in whole created by Russia — Bolshevik, Communist Russia, to be precise.”

Briefing reporters on the condition of anonymity on Monday evening, a senior administration official called Mr. Putin’s speech an address to the Russian people to justify war, and said the administration was under no illusions about what was likely to happen next.

But it is unclear that Mr. Putin cares about the next round of sanctions, believing that his economy can withstand anything Mr. Biden and other Western leaders throw at him. In his speech, he referred to Mr. Biden’s sanctions threats as “blackmail,” saying they would have been “put in place on Russia regardless of what happens in Ukraine.”

“The purpose,” he argued, is “to keep Russia behind, to prevent it from developing. And they will do it even without any formal pretext. Just because we exist.”

Mr. Putin’s winding, grievance-filled speech was filled with accusations that Ukraine was seeking its own nuclear arsenal — there is no evidence that is true — and that NATO was plotting to place Tomahawk missiles on Ukrainian territory, where they could strike Russia in minutes.

“I don’t doubt they are already calculating how to realize these plans,” Mr. Putin said.

American officials have said for months that there are no such plans, and Mr. Biden said at a January news conference that Ukraine was still years away from qualifying for NATO membership. But he has been unwilling to bend to Mr. Putin’s demand that NATO cease accepting new members, and that he provide a written, binding guarantee that Ukraine would never be part of the Western alliance.

Mr. Biden’s options for countering any military moves into Ukraine in coming days are limited. He has said repeatedly that he would not allow American forces to fight in Ukraine. But there is no guarantee that the conflict will not spill over Ukraine’s borders.

Europe was girding for refugees fleeing a modern, if corruption-ridden, democracy whose president, Volodymyr Zelensky, was in Munich on Saturday pleading his case that NATO must open its doors to his country — and thus defend it. Mr. Biden’s own national security officials have been warning American utilities, banks and other businesses to harden their networks against what they fear will be a wave of Russian-origin cyberattacks and ransomware, which they have publicly warned could be unleashed in reaction to the sanctions.

While Mr. Biden’s actions on Monday night were restrained, his administration denounced the Russian decision as a breach of the rules governing the global order.

In a statement, Jen Psaki, the White House press secretary, called Mr. Putin’s move a “blatant violation of Russia’s international commitments.”

The secretary general of the United Nations, António Guterres, called the action a violation of his organization’s charter. The United Nations Security Council planned to hold an emergency meeting on Monday night — but Russia holds a veto in that body, assuring that it could block any action.

In a joint statement, the European Commission president, Ursula von der Leyen, and the European Council president, Charles Michel, wrote that the European Union would “react with sanctions against those involved in this illegal act,” and that it “reiterates its unwavering support to Ukraine’s independence, sovereignty and territorial integrity within its internationally recognized borders.”

White House officials said Mr. Biden spoke with Mr. Zelensky for about 35 minutes after Mr. Putin’s speech. Ms. Psaki did not provide any details about the call, but said the United States was “continuing to closely consult with allies and partners, including Ukraine.”

Mr. Biden’s decision to hold back the full sanctions — for now — came as voices across the political spectrum called on Monday for the United States and its European allies to unleash the threatened economic measures on Moscow now, before Mr. Putin extends his control beyond the Donbas region of eastern Ukraine.

Mr. Putin’s “decision should immediately be met with forceful sanctions to destroy the ruble and crush the Russian oil and gas sector,” Senator Lindsey Graham, Republican of South Carolina and a longtime hawk on Russia, wrote on Twitter shortly after the Russian president concluded his remarks.

Even close allies of Mr. Biden like Senator Chris Coons, the Delaware Democrat who frequently consults with the president on foreign policy issues, said on Monday night that the time to hit Russia with economic penalties had begun.

“The time for taking action to impose significant costs on President Putin and the Kremlin starts now,”‘ he said in a statement issued as he toured Eastern European NATO nations. He said Mr. Putin “has made clear he intends to further invade Ukraine in a blatant effort to redraw the borders of Eastern Europe according to the whims of Moscow.”

Michael A. McFaul, who served as President Barack Obama’s ambassador to Russia, also urged Mr. Biden and the United States allies not to wait.

“Let’s be clear, this act is an invasion of the sovereign country of Ukraine,” he wrote on Twitter. “The West has to react forcefully, not ‘proportionally,’ and implement the full range of sanctions they have been promising.”