Seoul and Pyongyang have remained technically at war since the 1950s but South Korean President Moon Jae-In and North Korean leader Kim Jong Un agreed at a landmark summit last week to work towards a permanent treaty to replace a 65-year-old armistice agreement.
Diplomatic sources in Pyongyang have said there were rumours that the three had been relocated, but there had been no confirmation of their exact whereabouts.
Kim Hak-song and Kim Sang Duk were both arrested in the North a year ago. "We believe that Mr. Trump can take them back on the day of the US-North Korea summit or he can send an envoy to take them back to the US before the summit".
Kim was a professor at Pyongyang University for Science and Technology (PUST), the country's only privately-run academic institution.
Tony Kim's son said his father was teaching accounting at PUST.
North Korea is dismissing U.S. claims that Pyongyang hacked the database of the United Nations committee that monitors sanctions against the North as "nonsense", saying the Trump administration should instead be working toward peace.
Three Americans held in North Korea will be released
Kim Dong Chol was arrested in October 2015 and six months later was sentenced to 10 years of hard labor. The three men are Kim Dong-cheol, Kim Sang-deok and Kim Hak-seong.
Kim Dong Chul, 64, was arrested in October 2015 and has been serving a 10-year term with hard labor for alleged espionage.
The press release accredited to the DPRK mission to the United Nations is somewhat of a rarity: while it has attributed statements to itself in the last two years, the majority of the mission's press releases are typically reposted dispatches previously published by North Korea's Korean Central News Agency (KCNA).
Trump said last month his administration was fighting "very diligently to get the three Americans back" and US Secretary of State Mike Pompeo told ABC News he brought up the detainees during his secret meeting with Kim Jong Un in Pyongyang over Easter weekend.
U.S. officials insisted at the time that their release "must not be related or used to loosen the main issue of denuclearization", the source said.
North Korean officials said he contracted botulism, but U.S. doctors found no evidence to verify that claim.
"The welfare and safety of US citizens overseas is one of the highest priorities of the Department of State".