Other administrations, including President Barack Obama’s, secured the release of imprisoned Americans without promising a summit meeting or improved diplomatic relations. Over the past week, Mr. Trump had criticized the Obama administration for failing to secure the release of the three men, who had been held on charges of committing espionage or “hostile acts” against North Korea. Two of them were taken prisoner after Mr. Trump took office.

The three men include Kim Dong-chul, a businessman and naturalized American citizen from the Virginia suburbs of Washington. He had been sentenced to 10 years’ hard labor in April 2016 after being convicted of spying and other offenses.

Tony Kim, also known as Kim Sang-duk, was arrested in April 2017 while trying to board a plane to leave the country. He had spent a month teaching accounting at a Christian-funded school, Pyongyang University of Science and Technology.

Kim Hak-song, who volunteered at the school’s agricultural research farm, was arrested in May 2017. According to CNN, he was born in China near the North Korean border and emigrated to the United States in the 1990s, later returning to China and eventually moving to Pyongyang.

Speaking through a translator, one of the men recounted his time in captivity, describing long days in labor camps but adding that he had received medical treatment when needed. Their release bears a striking contrast to Otto F. Warmbier, a University of Virginia student who was returned to American custody in June after spending 17 months in captivity, much of it in a coma, in Pyongyang. He died days later.

From the tarmac, Mr. Trump acknowledged Mr. Warmbier and his family. “I want to pay my warmest respects to the parents of Otto Warmbier,” the president said, “who was a great young man who really suffered.”