The historic meeting between the two leaders will take place at the island resort of Sentosa on Tuesday.
He went out of his way to be cordial during two summits with South Korean President Moon Jae-in in April and May.
"The entire world is watching the historic summit between [North Korea] and the United States of America, and thanks to your honest efforts. we were able to complete the preparations for the historic summit", Kim told Lee through an interpreter.
Today, Sung Kim, a former United States ambassador to South Korea and former nuclear negotiator with the North, will lead a U.S. delegation for a working group with a North Korean delegation at the Ritz Carlton hotel, Ms Sanders said. Create peace and great prosperity for his land.
Some foreign-policy experts said the breakdown at the Group of 7 meeting would play to North Korea's advantage, since Mr. Trump can ill afford a second failed summit, back to back.
The pair are scheduled to meet at 9am local time on Tuesday, and will hold one-on-one talks for around two hours before being joined by their aides.
Mr Lee complimented the bold and admirable decision by Kim Jong and Mr Trump to come together for the Summit.
Sky News video showed the impressive motorcade that that carried Kim from the airport to his overnight lodgings.
"It's never been done before", Trump said of a U.S.
Brad Adams, Asia director at Human Rights Watch, said it was imperative that Trump bring up rights issues with Kim. The meeting was briefly canceled by Trump.
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Preliminary meetings have already begun.
The US president will arrive later today.
Kim's main concern is the survival of his own regime - South Korean President Moon Jae-in told reporters that the Pyongyang leader had "concerns on whether he could trust that the United States would end its hostile policy and guarantee the security of his regime when the North denuclearises itself".
The Singaporean delegation also surprised the U.S. leader with a birthday cake.
North Korea had also threatened to strike Guam, an American territory in the Pacific Ocean.
Trump continued to tweet angrily at Trudeau from Singapore, saying Monday "Fair Trade is now to be called Fool Trade if it is not Reciprocal". The leaders are spending the night at hotels about a half-mile apart in the upscale shopping area in Tanglin.
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"The best possible outcome I see for this summit is a general outline of an agreement that identifies denuclearization as the end goal of a process to be determined", she said at a 38 North briefing.
The summit would discuss "building a permanent and durable peacekeeping mechanism on the Korean Peninsula, the issue of realising denuclearisation of the Korean Peninsula" and other issues "as required by the changed era".
It is no easy task.
North and South Korea remain technically at war after the 1950-53 conflict ended in an armistice that Seoul's then leader refused to sign and divided the peninsula along the Demilitarized Zone.
Third, a peace treaty ending the Korean War must be initiated. The former businessman said he has spend a lifetime preparing for negotiations of this type, and predicted he would know in an instant if Kim is serious about the topic of denuclearisation. And if I think it won't happen, I'm not going to waste my time.
"I feel really confident".