After the much-ballyhooed summit in Alaska, anxious Europeans (including Ukrainians) can let out their bated breath. President Trump did not agree to hand over chunks of Ukraine to President Vladimir V. Putin of Russia, at least not yet, or to limit European aid to Kyiv.

Still, in comments after the meeting, Mr. Trump lavishly praised Mr. Putin and again put the onus for a deal on President Volodymyr Zelensky of Ukraine. After all, Mr. Trump said, “Russia is a very big power, and they’re not,” he told Fox News, referring to Ukraine.

“Now it is really up to President Zelensky to get it done,” he added. “I would also say the European nations have to get involved a little bit.”

Whether he meant that the Europeans should also pressure Ukraine to come to terms or that they should provide further aid and assurances to Kyiv was not clear. Mr. Zelensky said on Saturday that he would meet Mr. Trump in Washington on Monday.

But the outcome of the short Alaska meeting, with more talks to come, reveals an underlying problem for the Europeans. They have no strategy of their own for bringing the war to a close, let alone for defeating Moscow. Instead, they have been racing to keep up with the variable stances of Mr. Trump, trying to hold him to certain red lines that protect Ukrainian sovereignty and European security.

For Mr. Trump, the war in Ukraine, which he consistently blames on Mr. Zelensky, is an obstacle to his desired relationship with Mr. Putin. But for Europe, the fate of Ukraine is of strategic importance. If Ukraine collapses, European military and political leaders predict a Russian effort to test NATO in the following few years. If a militarized Russia can be held off — or even beaten back — it may end or retard Mr. Putin’s ambitions to upend the post-Cold War order and recreate the Soviet empire.