Analysts examining video of North Korea’s launch on Friday of an intercontinental ballistic missile that appeared capable of reaching the West Coast of the United States say they saw evidence of a setback the North never mentioned: The mock warhead on the missile shattered into pieces during its fiery re-entry to earth.

If the analysis is correct, it would mean that North Korea suffered a significant, but not decisive, setback. It suggests that the country, for all its success as it works toward its goal of putting American cities under threat, has not yet mastered the difficult aerodynamics of designing a warhead that can survive re-entry.

News of the video analysis came as President Trump, asked about the launch for the first time, offered vague assurances that he was on top of the problem. “We’ll handle North Korea,” he said, heading into a cabinet meeting. “We’re going to be able to handle them. It will be handled. We handle everything.”

Mr. Trump’s statements fell well short of describing a strategy, and his aides were working to develop an approach that goes beyond the largely symbolic flight of B-1B bombers over the Korean Peninsula last weekend in response to the test. The bombers accompanied South Korean and Japanese fighters, in a sign of solidarity.