But there was a surprising tenacity about taking on Mr. Putin — a sense that did not exist broadly across Europe until the invasion began, and that has only intensified since.

“I don’t think we have any choice,’’ Roberta Metsola, the president of the European Parliament, said as Mr. Biden moved from NATO headquarters to the headquarters of the European Union in his day of emergency meetings. “We know that any indecision or any differences will be exploited by Putin and his allies.”

Twice during the series of meetings, President Volodymyr Zelensky of Ukraine beamed in from his command post in Kyiv, telling the others that no matter how proud they are of how they have stood up to Mr. Putin, they have not done enough. Ukraine, he suggested, was fighting a war for Europe — and one that Europeans, as much as Ukrainians, could not afford to lose, because Mr. Putin would not stop at Ukraine’s borders.