Mr. Trump has signaled his preference to respond aggressively against the North Korean threat. In a Twitter post after Mr. Kim first issued his warning on New Year’s Day, the president wrote, “It won’t happen!” Yet like Mr. Obama before him, Mr. Trump is quickly discovering that he must choose from highly imperfect options.

He could order the escalation of the Pentagon’s cyber and electronic warfare effort, but that carries no guarantees. He could open negotiations with the North to freeze its nuclear and missile programs, but that would leave a looming threat in place. He could prepare for direct missile strikes on the launch sites, which Mr. Obama also considered, but there is little chance of hitting every target. He could press the Chinese to cut off trade and support, but Beijing has always stopped short of steps that could lead to the regime’s collapse.

In two meetings of Mr. Trump’s national security deputies in the Situation Room, the most recent on Tuesday, all those options were discussed, along with the possibility of reintroducing nuclear weapons to South Korea as a dramatic warning. Administration officials say those issues will soon go to Mr. Trump and his top national security aides.

The decision to intensify the cyber and electronic strikes, in early 2014, came after Mr. Obama concluded that the $300 billion spent since the Eisenhower era on traditional antimissile systems, often compared to hitting “a bullet with a bullet,” had failed the core purpose of protecting the continental United States. Flight tests of interceptors based in Alaska and California had an overall failure rate of 56 percent, under near-perfect conditions. Privately, many experts warned the system would fare worse in real combat.