Flanked by bodyguards, Kim also visited the Marina Bay Sands resort.
Just meeting Mr Trump will also give Mr Kim a recognition North Korea has long sought, setting him up as global player and the leader of a country worthy of respect.
After shaking hands with Singapore's foreign minister, Mr Kim sped through the streets in a limousine, two large North Korean flags fluttering on the auto, surrounded by other black vehicles with tinted windows and bound for the luxurious and closely guarded St Regis Hotel.
Commenting for the first time on the agenda, North Korea's state-run KCNA news agency said the two sides would exchange "wide-ranging and profound views" to re-set relations.
Experts on North Korea say that the shortened meeting time leaves nearly no room to forge a path for Pyongyang's "complete, verifiable, irreversible denuclearization", or CVID, which the US State Department was promising just last week. The national security adviser's previous remark that disarmament should follow the "Libya model" embraced by Moammar Qaddafi - who after giving up his nuclear weapons was later overthrown and killed in a US-backed uprising - prompted an angry reply from Pyongyang.
"If diplomacy does not move in the right direction ... those measures will increase".
U.S. Secretary of State Mike Pompeo, who is also in Singapore, said in a tweet that Washington was "committed to the complete, verifiable, irreversible denuclearisation of the Korean peninsula". He had earlier been scheduled to leave on Wednesday.
Mr Trump had earlier tweeted about the "excitement in the air".
Totalitarian North Korea's governing ideology of "Juche", which champions self-sufficiency, has brought little but decades of economic stagnation, widespread poverty and, at times, starvation.
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"I'm very optimistic we will have a successful outcome with the two leaders", he said. "The great risk is that Kim badly botches his meeting with Trump, other North Korean officials seem to be stalling, and the USA delegation gets the sense they are being taken advantage of".
A group of North Korean security staff were seen coming back into the hotel with cardboard boxes, one with McDonald's takeaway. Abbreviating the meeting to a single day could make it easier to cast the summit as an early, symbolic opening, rather than a substantive negotiation in which a lack of tangible progress would suggest failure on the part of the negotiators.
"If President Moon said he would come here to declare an end to war before the North-U.S. summit is held, it would, from the U.S. perspective, be like showing an entire answer sheet", the official said.
Trump also said he would not withdraw US troops from South Korea as part of the agreement, though he would like to "get our soldiers home" at some point. They believe Kim's latest engagement is aimed at getting the United States to ease the crippling sanctions that have squeezed the impoverished country.
"We'll probably need another summit", Trump said during the news conference that lasted more than an hour.
Despite the initial high stakes of a meeting meant to rid North Korea of its nuclear weapons, the talks have been portrayed by Trump in recent days more as a get-to-know-each-other meeting.
Now, Trump plans to hold his first meeting with Kim alone save for a pair of interpreters, heightening concerns he will stray from the approach United States officials hope the President will follow.
After greeting each other, the two leaders planned to sit for a one-on-one meeting that a United States official, speaking on condition of anonymity, said could last up to two hours, with only translators joining them. President Trump has described it as a "get-to-know-you situation" and said "it's going to be a process".
Later, they would be joined by their respective negotiating teams for discussions that could last another hour.