Kim Jong-un, North Korea’s leader, Mr. Trump explained recently, just “likes testing missiles.”

Now, American intelligence officials and outside experts have come to a far different conclusion: that the launchings downplayed by Mr. Trump, including two late last month, have allowed Mr. Kim to test missiles with greater range and maneuverability that could overwhelm American defenses in the region…

Mr. Kim’s flattery of Mr. Trump with beguiling letters and episodic meetings offering vague assurances of eventual nuclear disarmament, some outside experts say, are part of what they call the North Korean leader’s strategy of buying time to improve his arsenal despite all the sanctions on North Korea.

The rapid improvements in the short-range missiles not only put Japan and South Korea in increased danger, but also threaten at least eight American bases in those countries housing more than 30,000 troops, according to an analysis of the missile ranges by The New York Times. Such missiles, experts say, could be designed to carry either conventional or nuclear warheads.