In the lead up to the summit, North Korea, however, has rejected any unilateral nuclear disarmament, and its reference to denuclearisation of the peninsula has historically meant it wants the USA to remove its "nuclear umbrella" protecting South Korea and Japan, which it sees as a threat. The president planned to stop in Guam and Hawaii on the way back to Washington.
The president is now in Singapore, just hours away from his historic meeting with Kim.
Trump spoke only briefly in public on Monday, forecasting a "nice" outcome. But in the evening, he left the St Regis hotel and visited the Flower Dome at Gardens by the Bay with Singaporean Foreign Minister Vivian Balakrishnan. And Trump himself, the White House called a lid on the president and - just after lunch the day before, so he hasn't been seen out publicly.
No sitting USA president has ever met a North Korean leader. But there were scant details on what new commitments had been secured from Kim, even as Trump announced he would end the regular military exercises the U.S. conducts with South Korea.
In the lead up to the summit, North Korea rejected any unilateral nuclear disarmament, and KCNA's reference to denuclearisation of the peninsula has historically meant it wants the United States to remove its "nuclear umbrella" protecting South Korea and Japan.
While Trump was optimistic about prospects for the first-ever meeting of sitting U.S. and North Korean leaders, U.S. Secretary of State Mike Pompeo injected a note of caution, saying it remained to be seen if Kim was honest about his willingness to denuclearise.
Investors showed little concern over the swipes that Trump took at Canadian Prime Minister Justin Trudeau over the weekend and Monday.
It's not clear what the U.S. side has been able to extract from the North Koreans in terms of their willingness to get rid of their nuclear weapons or allow inspectors into the country to catalogue the scale of their program. "We've been waiting for one nation since we've been separated".
As he was trying to build a bridge with Kim, he was smashing longtime alliances with Western allies with his abrasive performance at the G-7.
Previous attempts to negotiate with Pyongyang have failed, but earlier this year North Korea demonstrated a new openness to diplomacy and held direct talks with Seoul.
Aware that the eyes of the world were on a moment many people never expected to see, Kim said that many of those watching would think it was a scene from a "science fiction movie".
He said secretary of state Mike Pompeo and defence secretary Jim Mattis should have opposed the one-on-one meeting "in writing" - and called for the national security council to have a transcript of all interactions with the "brutal, nuclear armed dictator".
The 45-minute talk between Trump and Kim was held privately.
Mattis added that discussions about US troop numbers on the peninsula would be "premature" ahead of the outcome of negotiations between the two leaders Tuesday.
The North has faced crippling diplomatic and economic sanctions as it has advanced development of its nuclear and ballistic missile programs.
Sanctions on North Korea would remain in place until that had happened, Pompeo said.
Experts believe the North is close to being able to target the entire USA mainland with its nuclear-armed missiles, and while there's deep skepticism that Kim will quickly give up those hard-won nukes, there is also some hope that diplomacy can replace the animosity between the U.S. and the North.
"This guy wants to be around the world, he wants to come to America, he wants to enjoy his life, he wants his people to enjoy this life", said Rodman, adding that Kim is "not a dumb man". Most importantly, few believe Kim is actually willing to give up the nuclear weapons that cement his grip on power. "That's what I do".
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