SEOUL, South Korea — With North Korea’s deadline for American concessions fast approaching, the North announced Sunday that it had conducted a “very important test” at a missile-engine site, rapidly ramping up pressure after months of carefully calibrated provocations.

Although President Trump has generally played down the North’s actions, on Sunday — just weeks before the Dec. 31 deadline — he issued a strong statement of his own, tweeting: “Kim Jong Un is too smart and has far too much to lose, everything actually, if he acts in a hostile way.”

Analysts said North Korea had most likely conducted a ground-based test of a new type of engine for long-range ballistic missiles. But the North did not yet describe the test or release pictures of it, as it has in the past, so it is unclear whether it was a success.

Still, if an engine was tested, analysts say it could be a warning that Mr. Kim is considering returning to long-range missile tests. It was a series of such launches in 2017 that provoked a crisis with the United States as it became clear that the North’s longest-range missiles were capable of reaching the West Coast of the United States, and perhaps beyond.