While North Korea blew up the entrances to its major underground testing site at Punggye-ri in May, it never allowed in inspectors, as promised, to determine whether the facility had actually been destroyed. Commercial satellite photographs suggest the buildings containing the control rooms and computers used to trigger and study the explosions were carefully mothballed.

And in the time between Mr. Trump and Mr. Kim’s first meeting, in Singapore in June, and their second in Hanoi, intelligence estimates suggest that North Korea produced enough uranium and plutonium to fuel a half-dozen new nuclear warheads.

The evidence that North Korea was moving ahead with its weapons program was clear, according to American intelligence officials familiar with the briefings provided to Mr. Trump. But the president sought to soften it in public to avoid imperiling negotiations, the officials said.