But China’s failure to do more to pressure North Korea — which was little surprise to anyone who follows the issue — also leaves the United States with few better alternatives to diplomacy. Some American officials had hoped to use the secret negotiations to obtain Mr. Warmbier’s release as the predicate for a dialogue with the North on other issues.

The tension between those who want to shelve engagement and take a much tougher line on North Korea and those who want to continue probing for openings is reflected in the administration’s ambivalent response after Mr. Warmbier was flown home in a coma last week.

At first, the White House and State Department said very little about the case, beyond expressing relief that he had been reunited with his family. But as outrage over the death of Mr. Warmbier, a 22-year-old college student, grew on social media and cable television, both released statements late on Monday condemning North Korea for his treatment.

Even on Tuesday, however, Mr. Trump appeared to place more of the blame on his predecessor, Barack Obama, for failing to negotiate Mr. Warmbier’s release than on Mr. Kim. “It’s a disgrace what happened to Otto,” the president said. “Frankly, if he were brought home sooner, I think the results would have been a lot different.”

But even as he implicitly criticized his predecessor, Mr. Trump appeared to walk away from one of the biggest gambles of his presidency. At a summit meeting in April at his Palm Beach, Fla., estate, Mar-a-Lago, Mr. Trump tried to enlist Mr. Xi to ratchet up China’s pressure on North Korea — something China has historically avoided because of fears that it would precipitate a collapse in a country with which it shares a 880-mile border.

The president made Mr. Xi the centerpiece of his strategy for North Korea, agreeing to soft-pedal his complaints during the 2016 campaign about China’s trade and currency practices in return for Beijing squeezing its neighbor to curb its nuclear and ballistic missile programs.