"We are having very good discussions," Trump said, ahead of a summit with the mercurial Kim expected sometime before the end of June.
"He really has been very open, I think -- very honorable."
"Now, a lot of promises have been made by North Korea over the years, but they have never been in this position," added the US leader, as he hosted his French counterpart Emmanuel Macron at the White House .
"We have been told directly that they would like to have the meeting as soon as possible," Trump said, adding: "We think that's a great thing for the world."
"We'll see where that will all go," he said.
Trump also reiterated that he would walk away from the talks with North Korea if they are not fruitful.
"Unlike past administrations, I will leave the table," he said. "But I think we have the chance to do something very special."
North Korea pledged last week to halt nuclear and missile tests as it prepares for a summit between Kim and Trump, but has not committed to giving up its atomic weapons -- which Pyongyang views as a shield against the Western overthrow of its government.
Kim is set to meet later this week with South Korean President Moon Jae-in -- the highest-level encounter yet in the whirlwind of nuclear diplomacy. APP/AFP