European allies of the United States have been trying to convince President Trump of the virtues of a shared approach toward ending the war in Ukraine, to enhance leverage on both Moscow and Kyiv and to preserve European security.

But Mr. Trump and Vice President JD Vance insisted on Wednesday that a set of proposals that their administration presented to the Europeans and Ukraine last week was now a kind of ultimatum, with the United States increasingly prepared to walk away. European officials who saw those proposals as too favorable to Russia and President Vladimir V. Putin face a dilemma.

If Mr. Trump sees Ukraine as just another crisis to fix or not, an obstacle toward a normalized diplomatic and business relationship with Mr. Putin, Europeans see the future of Ukraine as fundamental. At stake, European officials and analysts say, is the key principle of European security for more than 50 years — that international borders, however they were drawn after the end of World War II, should not be changed by force.

And those countries say they are prepared to keep supporting Ukraine should the Americans walk away.

“My sense is that Europe understands the stakes, and that Europe will continue to support the Ukrainian government,” Foreign Minister Radoslaw Sikorski of Poland said in an interview. “And Poland certainly will, and we’re not the only ones.”

Foreign Minister Radoslaw Sikorski of Poland estimates that the war has cost Russia at least $200 billion and killed or injured almost a million Russian soldiersCredit…Omar Havana/Getty Images