SEOUL, South Korea — North Korea’s vow to ignite an “enveloping fire” of test missiles near the American island of Guam is the first time it has specified a target with so much detail, escalating a showdown between Kim Jong-un, the North Korean leader, and President Trump.

For Mr. Kim, failure of the plan announced on Thursday, which includes precise details like splashdown points and exact travel times for four test missiles, would be a potentially costly blunder that could subvert his authority.

For Mr. Trump, whose dire warnings to North Korea — which he further escalated on Thursday — have echoed Mr. Kim’s own screeds, a successful North Korean test would be an embarrassment that could force him into exceedingly difficult choices about military action.

But North Korea’s prospective test also includes some maneuvering room for a possible compromise, South Korean analysts said. North Korea said the missile launches were still in the planning phase and would not be finalized until later this month, raising the possibility of delay or cancellation.