“He tells me that he didn’t know about it, and I will take him at his word,” Mr. Trump said on Thursday.

Mr. Warmbier, a student at the University of Virginia, was arrested while on a trip to North Korea for stealing a propaganda poster. In 2016 he was sentenced to 15 years hard labor.

More than a year later he was released and returned to the United States gravely ill, with doctors saying he suffered a catastrophic brain injury. He died in June 2017.

Mr. Trump has taken credit for the return of Mr. Warmbier and a handful of other Americans held in North Korea. In the past, the president has pointed to Mr. Warmbier’s injuries as an example of the Kim regime’s brutality.

But on Thursday, Mr. Trump refused to place any blame on Mr. Kim.

“I don’t believe that he would have allowed that to happen, it just wasn’t to his advantage to happen,” Mr. Trump said. “Those prisons are rough, they’re rough places, and bad things happened. But I really don’t believe that he, I don’t believe that he knew about it.”

—Austin Ramzy

A cheerful start gave no hint of trouble

Thursday began without any outward sign that talks were about to break down.

President Trump and the North Korean leader, Kim Jong-un, complimented each other in opening remarks at the Metropole Hotel in Hanoi. Neither predicted any imminent breakthroughs, but their comments did not suggest a summit meeting that would end early, abruptly, and without anything to show for it.

“I can’t speak necessarily for today, but I can say a little bit longer term and over a period of time I know we are going to have a fantastic success with respect to chairman Kim and North Korea,” Mr. he said.