Mr. Qaddafi gave up all the elements of his nascent nuclear weapons program in 2003, in return for promises of economic integration with the West. That never fully materialized. And as soon as there was an uprising against him, the United States, European allies and some Arab states bombed him. He was found by rebel forces and executed.

But perhaps more than a self-preservation strategy is at work here. Mr. Kim, some of Mr. Trump’s advisers and outside experts believe, thinks he may be able to force the United States to withdraw sanctions and pull back its troops from South Korea, where they are a perennial irritant to Pyongyang.

Where analysts diverge is what he might do if the United States really did withdraw some or all of its forces, as Mr. Trump’s former chief strategist, Stephen K. Bannon, suggested that Washington consider doing. One fear is that it could use its nuclear arsenal as a shield for a military invasion of South Korea in an attempt to reunify the peninsula by force.

The worry, say those who fear the North is considering that option, is that its ability to strike the United States with nuclear missiles could undermine Americans’ ability to guarantee that it would protect South Korea, as well as Japan, from attack.

“If the Americans face a choice between San Francisco and Seoul, they will choose San Francisco,” said Andrei Lankov, a North Korea expert at Kookmin University in Seoul.

Based on that calculation, Mr. Lankov said, North Korea “can provoke a conflict in South Korea and then they can just basically put an ultimatum to the United States telling the Americans that if they get involved, they are going to basically get a North Korean retaliation strike.”

Such a conflict would be catastrophic for Asia, and could lead to the loss of hundreds of thousands of lives. But it would also undercut every assurance the United States has made to other allies, from NATO to New Zealand, about coming to their defense.