Mr Trump and Mr Kim have had an extraordinary up-and-down relationship over the past 18 months, trading insults and threatening war before abruptly changing tack and moving towards a face-to-face meeting.
White House spokeswoman Sarah Sanders said USA and North Korean officials would hold working-level talks on Monday.
The North Korean leader smiled broadly Sunday evening as he met with Singapore Prime Minister Lee Hsien Loong.
North Korean leader Kim Jong Un impersonator Howard X (L) and Donald Trump impersonator Dennis Alan (R) make an appearance at the Merlion park in Singapore on June 8, 2018. The two are scheduled to meet for the first time Tuesday morning.
In their letter, Senate Minority Leader Chuck Schumer and Robert Menendez, the top Democrat on the Senate Foreign Relations Committee, called for any agreement with North Korea to meet five key points: that all weapons of mass destruction be removed or dismantled; that there be no uranium enrichment or plutonium reprocessing; that it end all ballistic missile testing; that it allow "anytime, anywhere" inspections of its facilities; and that a deal be permanent. "And he has that opportunity, and he won't have that opportunity again". "And obviously, what has been done before hasn't worked".
The men have tie-ups with several local businesses and will also make an appearance at a seafood restaurant.
As Trump's adviser and former NY mayor Rudy Giuliani told an event in Jerusalem last week hosted by OneFamily: "Now President Trump is on the verge of, hopefully, a breakthrough with North Korea".
Trump delivered off-script comments as he was leaving a G-7 summit in Canada, a meeting at which he was at odds with USA allies on issues such as trade.
Raising expectations in advance of the meeting, Trump said the outcome will rely heavily on his own instincts.
The summit is set to mark the first meeting between a sitting US President and a North Korean leader and comes after Trump and Kim previously engaged in a war of words over the North Korean nuclear program and each nation's military capabilities.
"I think I'll know pretty quickly whether or not, in my opinion, something positive will happen".
"The fact that we have been chosen as the site of the meeting... says something about Singapore's relations with the parties - with America, with North Korea - (and) also our standing in the worldwide community", said Lee.
The agency revealed that Kim flew in on a Chinese plane, provided for his "personal use", accompanied by a host of senior officials, including his influential sister, Kim Yo-jong.
In March, Mr Trump surprised the world by accepting an invitation from Mr Kim - delivered via Seoul - to meet in person. Asked by a reporter how he felt about the summit, Trump said: "Very good". Seeing Nobel Peace Prize laurels and eyeing potential to show up his critics at home and overseas, Trump is granting Kim the global legitimacy he's long sought in hopes of securing a legacy-defining accord.
In recent weeks, though, Trump's enthusiasm has been tempered somewhat by the challenge of deal-making with such an unpredictable opponent. In return for safeguards and potential economic help, Trump demanded "complete, verifiable and irreversible" destruction of North Korea's nukes.
Entrepreneurs have been scrambling to cash in on the worldwide media spectacle, hawking Trump-Kim fusion burgers and summit-themed cocktails.
After cutting short his participation over the icy reception, Trump veered within hours from espousing a great relationship with the US allies to tweeting that his host, Canadian Prime Minister Justin Trudeau, had been "Very dishonest & weak" in post-summit remarks.
Vice President Mike Pence said at a Christian nonprofit organization's conference in Washington, DC, on Saturday that he had spoken with Otto Warmbier's father earlier in the day and that Trump was going into the summit with "with the family of Otto Warmbier on his heart".
Officials who arrived with Trump include Pompeo, National Security Adviser John Bolton, White House Chief of Staff John Kelly and White House Press Secretary Sarah Sanders.
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After the conclusion of the summit, Trump again said he would not allow other countries to impose barriers on the United States. Relations between with the United States and the other members, particularly Canada, remained strained on the issue of trade.