The missiles were a shock in this western Ukrainian city spared from much of the war, a place so far from the front lines it does not even have a curfew. When the mayor heard the first strike, he thought it was thunder.

But the target and timing of the cruise missiles were even more surprising. They hit a factory run by an American multinational, best known for making coffee machines, six days after President Trump met President Vladimir V. Putin of Russia in Alaska to discuss ending the war in Ukraine.

“Two hits in one location?” asked Andriy Baloha, the mayor of Mukachevo. “No, they didn’t mess up. They knew exactly where they were hitting.”

A week later, two missiles hit central Kyiv, damaging the offices there of the European Union and the British Council, a cultural organization. Russia typically avoids striking that area, where foreign diplomatic missions are concentrated. Ursula von der Leyen, the president of the European Commission, accused Moscow of intentionally targeting the European Union.

Striking American and European assets, analysts and government officials said, sent a confrontational message: Mr. Putin feels empowered to rebuff pressure to make peace, to wage war as he sees fit, and even to inflict pain on the West in the process.

Mr. Trump has been calling for direct peace talks between Mr. Putin and President Volodymyr Zelensky of Ukraine, while European countries are discussing what security guarantees to provide Ukraine after the war to prevent another Russian invasion. The Kremlin has dismissed negotiations as premature and Western security guarantees as unacceptable.