And so the planning continues.

Mr. Mattis and other senior military leaders fear that a stray incident could spark a sudden conflict with the North. Of particular concern is the “ladder of escalation” — a chain of actions prompted by the shooting down of a North Korean or American jet, or sinking of a ship of which Mr. Mattis and other Pentagon leaders could quickly lose control.

Harsh new sanctions that the Trump administration announced last week are a prime example.

The economic penalties target 28 ships that are registered in China and seven other countries, and intend to further cut off North Korea’s imports of oil and exports of coal. But by going after the shipments, the United States is edging closer to the imposition of an economic blockade on the North.

While Treasury Secretary Steven Mnuchin stopped short of saying the United States Navy would forcibly board ships on the high seas, administration officials privately have said that sailors may yet be called upon to do so, if hostile foreign vessels are suspected of transporting certain material to North Korea.

That, Defense Department officials say, could easily spark an incident that could escalate.

Mr. Trump recently referred to another type of incident that American officials fear could spark a war.

During a speech in Seoul last year, he brought up North Korea’s 1969 downing an American spy plane that had been flying over the Sea of Japan. All 31 Americans aboard were killed in the attack by two North Korean MiGs.

At the time, President Richard M. Nixon chose not to retaliate. It is unclear if Mr. Trump would follow the same course; in bringing up the episode last year, he warned, “Do not underestimate us, and do not try us.”

The Hawaii planning exercise looked at a wide range of military capabilities and missions. They included:

■ How many conventional and Special Operations forces could be deployed, in phases, to target North Korean nuclear sites.