In an interview with CNN, Joseph Yun, who announced his retirement from the State Department in late February, said he also encouraged North Korean officials to respond to Trump's announcement that he will meet with Kim. No date or location for the talks has been announced, although they are expected to occur in late May.
Yun said he had delivered the message in talks with North Korean officials after Trump's announcement last week that he would be willing to meet face-to-face with Kim.
"I've talked to North Korea and I sent a single message to them, which was that this was an amazing opportunity for both sides and they need to respond," Yun told CNN.
"I pressed the point to them, this would be an incredibly good time for them to release those prisoners so that they can be reunited with their families. And that that in itself, I told them, would be a very positive message," he added.
South Korean-born Yun, a strong advocate for engagement with Pyongyang, led contact with North Korea and quietly pursued direct diplomacy since taking his post under former President Barack Obama in 2016.
The possibility of a summit has raised speculation it could lead to the release of the three Americans. They are: Kim Dong Chul, a Korean-American missionary; Kim Sang-duk, who spent a month teaching at the foreign-funded Pyongyang University of Science and Technology (PUST) before he was arrested in 2017; and Kim Hak Song, who also taught at PUST.
Yun said he hoped the summit would open the way to further talks on easing U.S. concerns over Pyongyang's nuclear programs.
"What I hope comes out of the summit is that President Trump and Kim Jong Un paint a broad-brush ... framework of where we need to go, and agree on some principles and agree to kick off a process," he said.
(Reporting by Lesley Wroughton; Editing by Leslie Adler)