Trump, who arrived Sunday night, tweeted Monday morning: "Great to be in Singapore, excitement in the air!" This is just an elaborate get-to-know-you session, albeit between the two most famous leaders in the world, and nuclear armed at that.
Hours earlier, a jet carrying Kim landed.
Trump's one-on-one meeting with Kim kicks off the first ever summit between a sitting USA president and a North Korean leader. The talks are expected to be devoted to the future of Pyongyang's nuclear program and the lifting of economic sanctions.
Although gaps remain over what denuclearisation would entail, Trump sounded a positive note in a lunch meeting with Singapore's Prime Minister Lee Hsien Loong.
Trump spoke only briefly in public on Monday, forecasting a "nice" outcome.
As many foreign policy experts, religious leaders, and human rights advocates have pointed out, denuclearizing the Korean peninsula is a critical security goal. The official was not authorized to speak publicly about internal deliberations and insisted on anonymity.
Kim Yong Chol's rise has baffled many North Korea watchers because he is the ruling Workers' Party official in charge of South Korea ties, not worldwide or US relations. He also has sought to lower expectations for the meeting, saying it may be the start of a longer process.
USA and North Korean officials are set to meet Monday morning in Singapore to make final preparations for Tuesday's meeting.
Following an on-camera greeting, the pair will begin the summit with a one-on-one meeting with only their translators, according to a senior Trump administration official.
After a sudden and welcome turn to diplomacy following last year's threats, insults and fears of war - remember "fire and fury" and "dotard"?
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The article also stresses the need for confidentiality - meaning Trump will have to resist tweeting the minutes of the meeting . The White House says Trump now plans to depart Singapore on Tuesday evening ahead of schedule.
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Following their meeting, President Trump will hold a media availability with reporters as Kim Jong Un departs back to North Korea.
Experts on North Korea say that the shortened meeting time leaves nearly no room to forge a path for Pyongyang's "complete, verifiable, irreversible denuclearization", or CVID, which the US State Department was promising just last week.
Part of the interest in Tuesday's summit is simply because Kim has had limited appearances on the world stage.
Since the first USA atomic test in the desert of New Mexico on July 16, 1945 eight countries have conducted an estimated 2,056 nuclear test explosions, mostly in the late 1950's and early 1960's - the darkest days of the Cold War, according to data from the Arms Control Association.
But it's Kim's pursuit of nuclear weapons that gives his meeting with Trump such high stakes.
Following that test, North Korea declared its state nuclear program was complete.
Trump's early exit will be his second from a summit in just a few days. China and South Korea would have to sign off on any legal treaty.
It's unclear what Trump and Kim might decide Tuesday.
Pyongyang has said it is willing to deal away its entire nuclear arsenal if the United States provides it with reliable security assurances and other benefits.
He explained that he gave the North Korean official Trump's book, "Art of the Deal", while he was in North Korea.
It was a striking about-face from less than a year ago, when Trump was threatening "fire and fury" against Kim, who in turn scorned the American president as a "mentally deranged USA dotard".