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.
Days earlier, in the North Korean village of Panmunjom, negotiations between diplomats from Washington and Pyongyang stalled when North Korea's vice-foreign minister Choe Son-hui said that denuclearization "should not be on the table for the Singapore summit" - a demand that would nullify the meeting's objective from the White House's perspective.
The Trump administration is pushing for Pyongyang to dismantle its nuclear weapons program, an action South Korea has said Kim is willing to take.
"I am on my way to Singapore where we have a chance to achieve a truly wonderful result for North Korea and the World".
"North Korea has previously confirmed to us its willingness to denuclearize, and we are eager to see if its words prove honest", he added.
He said if diplomacy fails to move in the right direction, the sanctions "will increase". "We're not going to go in and sign something on June 12, and we never were".More news: Explained: What is the UK's Trooping the Colour parade?
Trump thanked the prime minister for Singapore's efforts to host the summit, the first-ever between a sitting USA president and a North Korean leader, at a hotel on the city-state's resort island of Sentosa on Tuesday. He had earlier been scheduled to leave on Wednesday. He went out of his way to be cordial during two summits with South Korean President Moon Jae-in in April and May. After shaking hands with Singapore's foreign minister, Kim sped through the streets in a limousine, two large North Korean flags fluttering on the hood, surrounded by other black vehicles with tinted windows and bound for the luxurious and closely guarded St. Regis Hotel.
On the way back to his hotel, Kim walked along a promenade near the Merlion, a giant statue, and fountain, of a mythical creature, half lion, half fish - Singapore's unofficial mascot.
In a post on Twitter during his flight, Trump reiterated his optimism that the summit with the North Korean leader will be a success.
It's not just the logistics of Kim's trip that are unclear.
Kim smiled as he took a selfie with Singapore's Foreign Minister Vivian Balakrishnan at the scenic waterfront Gardens by the Bay.
He had his first formal meeting of the summit with the prime minister of Singapore, Lee Hsien Loong. As he says, "I'm optimistic that we will have a successful outcome" or words to that effect.More news: Platinum Games is making Babylon’s Fall for Square Enix
They also mention the goal of his trip, a "historic first meeting with the USA president", describing not only Mr Kim's itinerary but also the fact that he used a Chinese plane to fly to Singapore, rather than his own personal jet.
The commemorative coin issued ahead of the US-North Korea summit.
Those points were echoed in Monday's media coverage in North Korea, which stressed that the talks with Trump would focus on forging a relationship more in tune with what was described as changing times - most likely meaning the North's new status as a nuclear-armed state - and its desire for a mechanism to ensure lasting peace on the Korean Peninsula and, finally, denuclearisation.
The White House said Trump would hold a one-on-one meeting with Kim on Tuesday on the small island of Sentosa. They will be joined only by translators and will spend a couple of hours before admitting their close advisers to the meeting.
Many experts on North Korea, one of the most insular and unpredictable countries in the world, remain sceptical Kim will ever completely abandon nuclear weapons.
Trump, who is offering to reduce economic sanctions on North Korea in exchange for denuclearisation, also seemed to warn Kim that the summit is a "one-time opportunity" that should not be wasted.More news: Robert DeNiro Says 'F**k Trump' Twice At Tony Awards
"The process could be doomed before it begins". India, Pakistan and North Korea are not CTBT signatories.
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