The United States is by far Europe’s most important trading partner, and the prospect of worse trading conditions has left the European Union scrambling to negotiate. But the Trump administration has showed little appetite to strike a deal so far.

“In the end, as it is said, one hand cannot clap,” Maros Sefcovic, the trade commissioner for the European Union, has said.

That has left Europeans seeking to strike new alliances and deepen existing trading relationships. And concerns about President Trump’s shifting stance on military support have driven partners like the European Union and Canada closer together. Canada is already working toward providing industrial support for Europe’s rearmament push.

European Commission officials did not immediately comment on Mr. Trump’s post.