Authorities have beefed up security around the hotels where Trump and Kim (Saint Regis) will be staying.
"If a breakthrough is achieved, if peace comes, there will be a bountiful harvest, primarily of course within the Korean Peninsula but indeed for all the rest of us", he said.
Those deals could include an agreement to keep talking, with a commitment to work towards a final goal of dismantling all nuclear weapons on the Korean peninsula, and an announcement to end hostility. "They both get what they want".
He thanked Singapore's organisation of the summit as if it was "their own family affair".
White House spokeswoman Sarah Sanders said USA and North Korean officials would hold working-level talks on Monday. Trump said Saturday that the "minimum" outcome of Tuesday's talks will be establishing a "relationship" with the North Korean leader. They urged Trump to maintain a tough stance with Kim and his ally China, writing that any deal giving North Korea relief on sanctions without the ability to verify that it is dismantling its nuclear and missile arsenal "is a bad deal".
All trade deals could be off, China warns US
The talks were focussed on getting China to move ahead with its recent promises to increase energy and farm imports from the U.S. White House advisers, meanwhile, insisted on fundamental changes in ties between the world's two biggest economic powers.
Just meeting with Trump will also give Kim a recognition North Korea has long sought, setting him up as global player and equal to the USA domestically and, internationally, as the leader of a "normal country" worthy of respect. The conflict ended in an armistice which sealed the division of the peninsula. The test will be whether a deal has "verifiable elements of a denuclearization", to prove whether the North has dismantled its nuclear and ballistic missile programs.
Kim's full delegation has not yet been confirmed, but other prominent North Korean officials seen in photos included foreign minister Ri Yong Ho and Kim Chang Son - the man who has been in Singapore in recent weeks negotiating logistical details for the summit. China and South Korea would have to sign off on any legal treaty.
The US wants North Korea to give up its nuclear weapons but it is not clear what Pyongyang might want in return.
But after a cooling of the rhetoric, both sides began forging tentative contacts that eventually saw Mike Pompeo - the former head of the Central Intelligence Agency who is now secretary of state - meet Kim in Pyongyang.
"He's one of the best negotiators of all time and I'm looking forward to him adding to his historic success at the Singapore Summit", Rodman wrote.
"He would be there, he would be running his country, his country would be very rich", Trump said in May, noting that Libya "was a much different model" and not applicable in this case. "So this isn't a question of preparation".