The two then signed a joint statement.
The Associated Press reports Trump was originally scheduled to depart early Wednesday morning, however he will now leave Tuesday night after a day of meetings with Kim and other leaders of North Korea.
Trump also told reporters in a news conference in Singapore that Kim would be destroying a major missile engine testing site "very soon".
"Yesterday's photo op doesn't change the fact that a nuclear-armed North Korea is a threat to the security of the United States, our allies, and the world". Trump described the drills as "provocative" and "inappropriate".
The declaration took some South Korean and US military officials by surprise - though US Defence secretary Jim Mattis was not among them, with spokeswoman Dana White saying "there were no surprises".
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Staying in the hotel wing adjacent to the U.S. president, Mr Mohan had been sitting at the hotel lobby since 6:30 AM today to track the Donald Trump's movements.
The carefully-choreographed signing went slightly off script when it appeared Kim's team did not want him to use the provided pen.
That's a big concession to make, and one that caught many people by surprise.
A large contingent of Democrats criticized the president and his staff for tentatively granting a number of concessions to the North Koreans, including a pause on military exercises in South Korea and even meeting with Kim in the first place to lend his leadership legitimacy on the worldwide stage.
Kim was heard telling Trump through a translator: "I think the entire world is watching this moment". He most recently travelled there a year ago as a private citizen.
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The lightly regarded Gronkowski , dead last through the first half-mile, fittingly played the role of lead disrupter. Baffert complimented his team for helping the horse, which ran three major, testing races in five weeks.
The US has long held the view that North Korea's illegitimate military activities can't be traded away for its right to do legitimate military activities.
Kim reaffirmed that he would "work toward complete denuclearisation of the Korean peninsula", though there was no indication the two men had agreed on what that would mean.
Trump downplayed Beijing's role in the denuclearization process.
"South Korea is a little confused".
Lee added that while the government has been "cost conscious" in its approach to spending for the summit it has also worked to ensure that all operational requirements for the meeting - especially in terms of security - have been met.
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When asked about gender inequality at airlines in the Middle East, he retorted: "not in Qatar Airways". Al Baker clarified his position in an interview on Tuesday, before the company issues its statement.
A statement from Beijing today indicated its satisfaction with the outcome.