Another test by itself would not be that remarkable. The North is believed to have enough plutonium for eight to 12 weapons, and several years ago it revealed a new program to enrich uranium, the other fuel for a nuclear weapon.

But if the North Korean claim about a hydrogen bomb is true, this test was of a different, and significantly more threatening, nature.

In recent weeks, Mr. Kim, believed to be in his early 30s and determined to accelerate the nuclear weapons program that his grandfather and his father promoted to give the broken country leverage and influence, boasted that North Korea had finally developed the technology to build a thermonuclear weapon.

When Mr. Kim first made the claim, in December, the White House expressed considerable skepticism, and several other experts say that the accomplishment would be a stretch, though not impossible.