WASHINGTON — North Korea’s detonation of a sixth nuclear bomb on Sunday prompted the Trump administration to warn that even the threat to use such a weapon against the United States and its allies “will be met with a massive military response.’’

The test — and President Trump’s response — immediately raised new questions about the president’s North Korea strategy and opened a new rift with a major American ally, South Korea, which Mr. Trump criticized for its “talk of appeasement” with the North.

The underground blast was by far North Korea’s most powerful ever. Though it was far from clear that the North had set off a hydrogen bomb, as it claimed, the explosion caused tremors that were felt in South Korea and China. Experts estimated that the blast was four to sixteen times more powerful than any the North had set off before, with far more destructive power than the bombs dropped on the Japanese cities of Hiroshima and Nagasaki during World War II.

Yet after a day of meetings in the Situation Room involving Mr. Trump and his advisers, two phone calls between the president and Prime Minister Shinzo Abe of Japan, and even demands from some liberal Democrats to cut off North Korea’s energy supplies, Mr. Trump’s aides conceded that they faced a familiar conundrum.