The risks for both Trump and Kim are significant, although the North Korean leader already has gotten what his predecessors did not, which is a meeting with the president of the United States. As a rule, they would only report on the leader's movements after the event.
Trump has downplayed what will come from the meeting, and told reporters last week that it is likely to be just the start.
Trump has also raised the possibility of further summits.
The two men later emerged from their meeting looking relaxed as they walked the open-air corridors.
"It's not like the Trump-Kim summit will solve everything", he added. To some national security veterans, it raised concerns about the risk of holding such a monumental meeting solo.
The media were then ushered out of the room. The huddle will come before a larger meeting and a working lunch attended by top advisers to the president and their North Korean counterparts.
However, Trump and his aides insist that a US-led "maximum pressure" campaign of the toughest-ever economic sanctions, diplomatic action and military threats is what has drawn Kim to the negotiating table.
The US insists it will accept nothing less than complete denuclearisation of the Korean peninsula. No, no, say others, you need to manage your expectations.
The two leaders, who initially looked cautious, were later seen more relaxed.
A transport plane - one of three aircraft that headed to Singapore - also carried food and Kim's bullet-proof limousine. Both leaders would offer "clear, specific, unequivocal statements" outlining a dismantlement of North Korean weapons, an inventory and removal of all nuclear fuel and an opening up to United Nations nuclear inspectors. Trump has expressed some concern about China's influence.
The smiles on Tuesday "don't mean anything" unless they are followed by specific commitments to make change in North Korea, Mr. Pinkston said.
Probably. In fact, Trump has been doing quite a bit of this lately.
The Hill has reached out to the White House for comment. He described it as a "get to know you plus" meeting. "The 'plus" refers to discussions on ending the Korean War".
Amateur body language analysts noted that Trump is being more physical than Kim.
Singapore, doing its bit to promote peace, has said it expects to spend about S$20 million ($15 million) on hosting the summit, including the North Koreans' hotel bill, Singapore's foreign minister told the BBC. "We can go fast, we can go slowly", Trump said.
Observers in the region warn that ultimatums over denuclearization could make military confrontation between the US and North Korea even more likely, a situation Zhao Hai from China's Academy of Social Sciences described as a "down-spiral of security" that could turn into a nuclear "nightmare".
Former NBA star Dennis Rodman - one of the few Westerners to have met the North Korean leader on visits to the capital city of Pyongyang - is in Singapore.
Both North Korea and the US have nonetheless sought to set expectations high. Trump responded to that criticism Tuesday on Twitter, saying: "The fact that I am having a meeting is a major loss for the USA, say the haters & losers".
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