Behind the new assessment, officials said, was a growing recognition that they underestimated the determination of Kim Jung-un, North Korea’s leader, to race ahead with a weapon that could reach American soil, even if it is crudely engineered and inaccurate.

General Paul Selva, the vice chairman of the Joint Chiefs of Staff, put the best case forward last week when testifying before the Senate Armed Services Committee. The most recent test, he said, stopped short of demonstrating that North Korea possesses “the capacity to strike the United States with any degree of accuracy or reasonable confidence of success.”

But that statement went far beyond what most Pentagon officials had been allowed to say in public before the most recent test. And it reflects a growing view, from the Defense Intelligence Agency to the C.I.A., that at this point Mr. Kim’s missile engineers, while still refining the technology, have cleared most of the major hurdles.

It is unclear how, if at all, that will change the calculus for President Trump. He has vowed to dispense with the Obama-era strategy of “strategic patience” toward North Korea. American military officials have been asked to come up with new potential strategies, from stepped-up economic pressure to increased cyber attacks on the missile testing regimes. But there is a lurking sense, one senior intelligence official said last week at the Aspen Security Forum, that at this point the best the United States can do is delay the day when North Korea demonstrates it can reach beyond Alaska and Hawaii.

“It’s a big long supply chain to build this thing out,” the director of the Central Intelligence Agency, Mike Pompeo, said at the security conference, the first public reference to a long-running covert program to undermine the parts and technologies that flow into North Korea. “As for the regime, I am hopeful we will find a way to separate it” from its missile and nuclear capabilities.