After a one-on-one meeting and a working lunch, Trump showed Kim the inside of his presidential vehicle.
As the two men walked off together through a high-ceilinged colonnade, Kim appeared to relax, flashed a smile and seemed to say something.
It was not immediately clear what specific progress, if any, had been made in preliminary discussions between U.S. and North Korean officials.
Even before the two leaders had left their separate city centre hotels and driven the 13 minutes through blocked-off police-lined roads to the island summit venue, the U.S. president used Twitter to claim victory and hit back at his critics.
Trump said he expects the talks to be a "tremendous success" adding, "We will have a tremendous relationship, I have no doubt". "We will be fine!"
Yet even as he turned his attention to the summit, Trump continued his blistering attacks on Canadian Prime Minister Justin Trudeau, tweeting: "Fair Trade is now to be called Fool Trade if it is not Reciprocal".
Trump and Kim met privately from 9:05am local time for 48 minutes flanked only by their translators, then broke for a wider bilateral meeting with aides, a meeting expected to last 90 minutes, leading into lunch at 11:30am (3:30 GMT). "We will all know soon whether or not a real deal, unlike those of the past, can happen!" he wrote.
Representatives from the White House Correspondents' Association, The AP, Reuters and Bloomberg did not immediately respond to a request for comment.
Kim also appeared to be focused on his own domestic audience, albeit it one without a vote.
Before a one-on-one meeting with only the interpreters present, there was another photo op as the two leaders shook hands across a coffee table and beamed at the assembled press. It was highly unusual for state media to report on worldwide events so speedily and to display the prosperity of other Asian nations so prominently. As the site for their meeting, the two leaders have chosen one of Singapore's most luxurious hotels, the Capella Resort on Sentosa Island, a popular vacation spot off the southern tip of Singapore and home to Universal Studios Singapore.
"The only way to know if North Korea's declarations are accurate is to verify them through on the ground presence", said David Albright, a former weapons inspector.
For both men, the summit, the first between leaders of North Korea and the United States, is likely to be a defining moment of their careers. "We appreciate your hospitality and professionalism and your friendship".
"One can imagine either approach making sense under certain circumstances", Walsh said. "Today, I think Trump has moved closer to the relationship approach".
Trump and Kim will first sit down for a one-on-one meeting accompanied only by personal translators.
For Kim, about half Trump's age and representing the third generation of North Korea's ruling dynasty, the summit affords both him and his long-isolated country the global legitimacy his father and grandfather could only dream of.
While the president has more recently sought to temper expectations of what he may be able to achieve with the summit, he has also said the interaction amounts to a crucial test in determining whether Kim is genuine in committing to rid his country of its nuclear program.
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