Tusk, however, expressed the acute concern of a leader with a new, unpredictable conflict suddenly on his doorstep, saying that Russian President Vladimir Putin’s intervention in Ukraine “increases the risk in Eastern Europe, but it also has global implications.”

“It is a challenge for the whole world,” Tusk said. “It is not just Poland, but all of Europe must speak in a strong voice.”

Tusk’s remarks captured the mounting worries sweeping through Eastern Europe as Putin resists international calls to withdraw from Crimea, a strategically important Black Sea peninsula with historic connections to Russia.

Over two days, Biden will meet with the leaders of Poland, Estonia, Latvia and Lithuania — all NATO members with old memories of Soviet domination and new fears of an expansionist Russia under Putin.

As Putin told Russia’s political leadership in Moscow that Crimea would again be part of Russia, Biden outlined the steps the United States intends to take to prevent that and head off a broader military push into eastern Ukraine. Such an escalation would bring the conflict even closer to Poland and the Baltic states.

Putin’s actions follow a referendum Sunday in which Crimean voters — under the eye of Russian troops — chose to split from Ukraine and join Russia.

During Biden’s visit, which included a meeting with visiting Estonian President Toomas Hendrik Ilves, Biden called Putin’s intervention in Ukraine a “brazen, brazen military incursion.” He told each leader that the Obama administration is committed to Article 5 of the NATO pact, calling for collective self-defense if one nation is attacked.

“If the international community does not stand up, then the international community will collapse,” Ilves said. “The kind of behavior we see is dangerous for the world.”

One senior administration official, speaking on the condition of anonymity to talk about the vice president’s plans, said Biden will discuss measures to be taken “in the days and weeks ahead,” building on financial sanctions imposed on 11 Russian and Ukrainian officials that President Obama announced Monday.

The talks here and on Wednesday in Vilnius, the capital of Lithuania, come days before European leaders are scheduled to meet in Brussels to consider Russia’s actions. Ilves urged European leaders to formulate a stronger response.

“The response should not be about the price of gas,” he said. “It should be about common values, and the price of not adhering to those values.”

The senior administration official said Biden will emphasize that whatever steps follow the sanctions announced by the United States and European Union must be taken “so that NATO emerges from this crisis stronger than when it went into it.”

Russia’s recognition of an independent Crimea, and Putin’s apparent step toward Russian annexation of the Black Sea peninsula, have proved to be a test of the Obama administration’s preference for economic sanctions and international diplomatic pressure over military threats.

Obama has sought to reenergize NATO, placing the alliance at the center of efforts to wind down the war in Afghanistan and act together in humanitarian emergencies such as in Libya in 2011. Poland and Lithuania convened an emergency meeting of NATO members this month in response to Russia’s move on Crimea.

But some allies, including in Europe, have watched with worry as Obama, in their view, has emphasized reaching out to antagonists at the expense of longtime friends. Administration officials strongly disagree, arguing that new relationships with such countries as China, Iran and Russia benefit U.S. allies in Europe and other regions.

How Obama intends to confront Putin has been closely monitored here and throughout Eastern Europe, a region deeply susceptible to Russian economic sanctions, energy disruptions and military threats. Obama has made clear that direct military engagement is not under consideration, although he has moved U.S. Navy ships closer to the Black Sea, where Russia maintains its only warm-water port.

Biden emphasized Tuesday that the United States has deployed 12 F-16 fighter jets to Poland in recent weeks and delivered 10 F-15s to the Baltic states for air-patrol programs. He announced additional U.S. military training for Poland’s army.

But Biden did not offer changes to administration plans for a missile-defense system in Eastern Europe, which Obama adjusted upon taking office at a time he was pursuing a “reset” in Russian relations.

Since Russia’s intervention in Ukraine, some congressional Republicans have called on Obama to return to the previous missile-defense plan negotiated by the George W. Bush administration. That plan would have placed a radar station in the Czech Republic and stationed 10 ground-based interceptors in Poland.

Obama chose instead to place interceptors on Navy ships. Over the next four years, NATO intends to put smaller ground-based interceptors in Romania and Poland.

The senior official said Biden will tell Eastern European leaders during his meetings that those missile-defense plans remain “on track” and will not be altered to respond to Russia’s actions in Ukraine.

“That is our commitment — an operational missile-defense system by 2018 here in Poland,” Biden said.

Appearing with Biden at the presidential palace, Polish President Bronislaw Komorowski said Russia has increased military spending 400 percent over the past eight years while some NATO members had cut defense spending. Biden responded, “You have an ally whose budget is larger than the next 10 nations in the world combined.”

“So don’t worry about where we are,” he said. “The United States has more than stood up to its responsibilities.”