“I do want to talk about our readiness, and ensure the things that we need to do to be prepared if diplomacy fails,” Mr. Shanahan told reporters aboard his plane to Seoul, the South Korean capital. But, he added, “I’m confident that we have the readiness that we’re required to have.”

The decision to continue offering the concession to North Korea came despite missile tests that Pyongyang conducted last month, and amid unconfirmed reports that North Korea has executed its special envoy to the United States on spying charges. A South Korean news daily also reported that Mr. Kim had ordered a sweeping purge of the country’s top nuclear negotiators after the breakdown in Hanoi, Vietnam, of his second summit meeting with Mr. Trump.

Still, after the failed meeting, which ended without an agreement on how, or whether, to shut down the North’s nuclear weapons program, Defense Department officials said the Pentagon would once again suspend two large-scale joint military exercises that were scheduled for this spring, to maintain the truce that Mr. Trump had struck with Mr. Kim.

But American military officials have long cautioned that suspending exercises can hamper readiness, so Mr. Shanahan is walking a tightrope as he tries to placate his boss, who has taken a more benign approach toward Mr. Kim in the past year, while reassuring commanders that they will have the tools they need to keep troops prepared.

In June last year, without consulting the Pentagon, the president suspended major military exercises with South Korea after meeting Mr. Kim for the first time, in Singapore. Two months later, Mr. Trump rebuked Jim Mattis, then the defense secretary, for opening the door to resuming the exercises.