At a news conference on Wednesday, Mr. Trump acknowledged the “harsh treatment” of what he called the “three prisoners” and pledged action.
“We have been talking about them,” he said. “We’re negotiating now. We are doing our very best.”
He added: “We fought very hard to get Otto Warmbier back. And when we came back, he was in very, very bad condition. It was a very sad event. We are likewise fighting very diligently to get the three American citizens back. I think there’s a good chance of doing it.”
A White House adviser, Matthew Pottinger, told reporters this week that the three Americans were a priority.
Here is what is known about the three detainees.
Kim Hak-song, also known as Jin Xue Song, was arrested on May 6, 2017. He worked at Pyongyang University of Science and Technology, and it was not clear whether his arrest was connected with that of his colleague Tony Kim two weeks earlier.
The university said in a statement that he had been doing agricultural development work at its research farm and was arrested after a trip there.
According to CNN, Mr. Kim, an ethnic Korean, was born in Jilin, China, near the North Korean border, and emigrated to the United States in the 1990s. After becoming an American citizen, the network said, Mr. Kim returned to China and studied agriculture at Yanbian before moving to Pyongyang, the capital.
Tony Kim, also known as Kim Sang-duk, was arrested on April 23, 2017. He had spent a month teaching accounting at Pyongyang University of Science and Technology and was trying to board a plane to leave the country when he was arrested, according to the chancellor of the university, Chan-Mo Park.
“The cause of his arrest is not known, but some officials at P.U.S.T. told me his arrest was not related to his work at P.U.S.T.,” Mr. Park told Reuters. “He had been involved with some other activities outside P.U.S.T., such as helping an orphanage.”
Mr. Kim, who is in his 50s, had previously taught at Yanbian University of Science and Technology, an affiliated institute in the Chinese province of Jilin, near the North Korean border. He had most recently been living in North Korea with his wife, who is believed to still be in the country.
Mr. Kim studied accounting at the University of California, Riverside and at Aurora University, and worked as an accountant in the United States for more than a decade, according to his Facebook page.
Kim Dong-chul, a businessman, was sentenced to 10 years of hard labor in April 2016 on charges of spying and other offenses.
A month before his trial, Mr. Kim appeared at a government-arranged news conference in Pyongyang and apologized for what he described as his attempted theft of military secrets in collusion with South Koreans. The South Korean spy agency has denied any involvement.
Mr. Kim’s predicament was not known until January 2016, when the North Korean government let CNN interview him in Pyongyang. At that time, Mr. Kim identified himself as a 62-year-old naturalized American citizen who lived in Fairfax, Va. He said he had once run a trading and hotel services company in Rason, a special economic zone near North Korea’s borders with China and Russia.
He said he was arrested in October 2015 while meeting with a former North Korean soldier to receive classified data.