Meeting with staged ceremony on a Singapore island, Trump and Kim came together for a summit that seemed just unthinkable months ago, clasping hands in front of a row of alternating USA and North Korean flags, holding a one-on-one meeting, additional talks with advisers and a working lunch.
But when pressed by reporters, the secretary of state would not say whether that could include reduction of the number of or removal of USA troops in South Korea.
"This is going to lead to more and more and more", Trump said.
But, with cameras of the world's press trained on them, they displayed an initial atmosphere of bonhomie as they met on the verandah of the Capella, a refurbished 19th century British regimental officers' mess.
In what looks like a victory for American big-stick diplomacy Kim agreed to wind down his nuclear ambitions so long as the United States promised not to attack his country.
Trump is hoping to make a legacy-defining deal that some say could earn him a Nobel Peace Prize.More news: Trump says he may pardon late boxing hero Muhammad Ali
-North Korea summit, is expected to pick up a considerable portion of North Korean leader Kim Jong-un's bills.
"I think the entire world is watching this moment".
"Very good, very good".
Kim also sounded positive about the prospects of peace. The former National Basketball Association player visited Pyongyang five times since the North Korean leader took charge. But I believed in North Korea.
The dollar jumped to a 3-week top on Tuesday and Asian shares rose on the news.
The two leaders met for about 40 minutes and were joined only by interpreters.More news: Neal Boyd Dead - 'America's Got Talent' Winner Dies at 42
The White House said the daylong summit would also include a working lunch and a larger meeting involving aides to both leaders.
The North Korean leader then traveled to the St. Regis Hotel - where he will be staying for the duration of the visit - in his armored limousine, which arrived on a separate flight.
"Trump clearly has the upper hand here because the media in North Korea is so tightly controlled. We'll have to see the concrete steps that North Korea takes", she said. "But they'll come off - as you know and as I have said, the sanctions right now remain but as a certain point I actually look forward to taking them off and they'll come off when we know we're down the road where it's not going to happen, nothing is going to happen".
Many analysts have suggested that the discussion about denuclearization means very different things to North Koreans than it does to American officials.
South Korean leader Moon Jae-in was barely able to sleep the night before.More news: Trump, Kim make history with first-ever US-North Korean summit
"We are hopeful this summit will have set the conditions for future successful talks", Pompeo said on Monday evening.