"I'm very optimistic that we will have a successful outcome from our meetings tomorrow", he said.
At the start of the summit, the two leaders who once threatened each other with nuclear annihilation shook hands on a red carpet in front of the island resort hotel chosen for the meeting. "I have no doubt".
The pair made brief remarks as they sat together before the world's media as the historic summit got under way, with the United States leader insisting "we will have a terrific relationship I have no doubt".
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"I believe we're going to have a terrific success or a modified success", Trump said during a press conference last week with Japanese Prime Minister Shinzo Abe. "And it's my honor to be involved".
The US doesn't recognise the Democratic People's Republic of Korea, nor do American officials have much reason to take North Korean leaders at their word, having had previous diplomatic efforts to engage scuttled.
Critics of Trump, however, were quick to point out that the USA president had given legitimacy to a murderous regime responsible for the starvation and death of tens of millions of people.
The meeting is also a striking departure for a relationship that just months ago was defined by highly personal insults and rhetoric that seemed to raise the possibility for imminent military confrontation. That is, experts suggest Pyongyang may only agree to give up its nukes in exchange for the USA terminating its military presence in South Korea and ending its regional nuclear umbrella, a security arrangement in which Washington promises in-kind retaliation on behalf of close allies if they are attacked with nuclear weapons.
After some initial exchanges lasting around 40 minutes, Trump and Kim emerged, walking side-by-side through the colonnaded hotel before re-entering the meeting room, where they were joined by their most senior officials.
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Reacting to the news of the two leaders meeting, basketball star and unlikely North Korea envoy Dennis Rodman, who is also in Singapore, said holding the summit was the right thing to do.
As for Singapore, the White House said Trump was leaving early because negotiations had moved "more quickly than expected" but gave no details.
It is also unclear whether US officials will raise human rights issues in meetings with the North Koreans.
There will not be a repeat of "flimsy agreements" made between previous US administrations and North Korea, Secretary Pompeo told reporters in Singapore on Monday.
Washington is eager to see if the North's pledges were "sincere", Pompeo said, adding: "The US has been fooled before".
Previously, Trump had derided Kim as "Little Rocket Man" and pledged to rain "fire and fury" on North Korea if it continued to make nuclear threats.
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