SEOUL, South Korea — As North Korea warned foreigners on Tuesday that they might want to leave South Korea because the peninsula was on the brink of nuclear war — a statement that analysts dismissed as hyperbole — the American commander in the Pacific expressed worries that the North’s young leader, Kim Jong-un, might not have left himself an easy exit to reduce tensions.

“His father and his grandfather, as far as I can see, always figured into their provocation cycle an ‘off ramp,’ ” the commander, Adm. Samuel J. Locklear III, said during testimony before the Senate Armed Services Committee. “And it’s not clear to me that he has thought through how to get out of it. And so that’s what makes this scenario, I think, particularly challenging.”

The administration has settled on a strategy of refusing to make concessions to the North and has adopted a new plan to deter any hostilities by promising a proportionate response. In doing so, it hopes to reverse what it considers a long-term pattern in which the West offers aid to calm tensions and then North Korea breaks its promises to halt its nuclear program. But Obama administration officials acknowledge that the new strategy will work only if Mr. Kim either backs down or satisfies himself with a token show of force, like a missile test into the open ocean. The South Koreans have warned such a test could happen as early as this week.

At the core of the concern within the administration and the intelligence agencies is that they do not understand Mr. Kim’s motivations. His father and grandfather suggested, at times, that they might be willing to negotiate to end their nuclear program. But Mr. Kim arrived in power with a small nuclear arsenal — the fuel for about six to a dozen weapons, according to intelligence officials, and a pathway to make more — and he may be calculating that with those potential weapons in hand, he is less vulnerable to attack.