A long-planned gathering in a Budapest sports arena took on unexpected urgency on Thursday as European leaders contended with the election victory of Donald J. Trump and the collapse of Germany’s ruling coalition, two pressing issues that added to the tumult of a world already thrown off balance by the war in Ukraine.

Adding to the drama was the fact that the meeting was being held in Hungary, whose authoritarian prime minister, Viktor Orban, has long been at odds with mainstream European leaders and is an ardent supporter of Mr. Trump.

Mr. Orban, without specifically mentioning Mr. Trump or Ukraine, made clear the import of the gathering of more than 40 heads of state and government leaders from the European Union, Ukraine and beyond. “The answers we give now may determine the future of Europe for decades,” he said.

Many of the leaders, despite offering Mr. Trump congratulations for his election triumph, are deeply anxious over what the former president’s return to the White House might mean for American security, trade and foreign policy.

Particularly concerned is President Volodymyr Zelensky of Ukraine. Stony-faced, he exchanged a frosty handshake with Mr. Orban, who has repeatedly called for an end to the war in Ukraine on terms similar to those proposed by Russia.

It was Mr. Zelensky’s first visit to Budapest since Russia began its full-scale invasion of Ukraine in February 2022 — a measure of the chilly relations between the two neighbors. Hungary joined European sanctions against Russia but vociferously denounced them, opposed military aid to Ukraine and sought to rally other European Union countries to what Mr. Orban calls a “peace agenda.”