Before the announcement, U.S. Secretary of State Mike Pompeo seemed to hint that the outcome of the talks might not be what Trump has promised in the past.
During a sendoff ceremony at Pyongyang International Airport, Kim boarded a Chinese plane provided for his personal use after greeting senior officials who came to bid him farewell, KCNA reported.
"We are hopeful this summit will have set the conditions for future successful talks", Pompeo said, describing a far more modest goal than Trump had outlined days earlier. Trump had earlier tweeted about "excitement in the air!"
"The entire world is watching the historic summit between (North Korea) and the United States of America", Mr Kim told Mr Lee through an interpreter when they met Sunday. Kim finished off the night with a walk along a pedestrian bridge near the city's Merlion Park.
Yet the top U.S. diplomat added Trump is ready to offer "unique" guarantees to ease the regime's concerns about giving up a nuclear arsenal that provides a deterrent against foreign adversaries while also serving as a key point of national pride.
While en route to Singapore, Trump said he looked forward to meeting Kim on what he anticipated would be an exciting day.
Preliminary meetings have already begun.
Kim is not believed to have left his hotel since a meeting with Singapore's prime minister, Lee Hsien Loong, soon after his arrival on Sunday in the city-state.
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Trump had been scheduled to fly back to Washington on Wednesday morning after spending Tuesday with the North Korean leader in Singapore.
Reunification, he said, would be impossible because four powers - the US, China, Russia and Japan - do not want to see a unified Korea.
A government described as authoritarian by its critics has clamped down on protests thought strict loitering laws and a hard permitting process. Trump and Kim lookalikes held a summit of their own at a local shopping mall, while one bistro is offering a libation known as the Trump-Kim "Bromance:" Beer, tequila, diet Coke and the Korean distilled rice liquor known as soju. Trump traveled to Singapore from Canada, where he attended a meeting with other world leaders. The president also refused to sign a G-7 joint statement pledging cooperation.
Top members of Trump's administration have said that the North Koreans wouldn't receive any benefits before taking steps to denuclearize - wary of falling into the same predicament that doomed previous agreements with the rogue regime.
It is no easy task.
"North Korea has previously confirmed to us its willingness to denuclearize, and we are eager to see if its words prove honest", he added. "The 'plus" refers to discussions on ending the Korean War".
Kim Yo Jong gained notoriety at the Winter Olympics in South Korea.
"I have little expectation from the summit", he said. "It's not a one meeting deal", he said.
"Just my touch, my feel", Trump replied.
He said his perception of Kim - a "bad guy with nuclear weapons" - had improved considerably following his two meetings with South Korean President Moon Jae-in at the border truce village of Panmunjom.