Trump said "we've got a very interesting meeting in particular tomorrow, and I think things can work out very nicely".
"If the summit becomes a success, the Singaporean efforts will go down in history", Kim said.
On Monday, North Korean state media said Kim and Trump would discuss a "permanent and durable peace-keeping mechanism" on the Korean peninsula, denuclearisation of the peninsula and other issues of mutual concern.
The report notes the summit is being held "under the great attention and expectation of the whole world".
North Korean and U.S. negotiators met in Singapore today for final preparations on the eve of an unprecedented summit between Kim Jong Un and Donald Trump, seeking to bridge the gaps over Pyongyang's nuclear arsenal.
Earlier this month, Singapore's defense minister said the USA trade threats were as disruptive to the global order as China's military deployments in the disputed South China Sea.
The meeting is kicking off at 9 a.m. on Tuesday with a handshake between Mr. Trump and Mr. Kim.
Kim Hyo-sun, Arirang News.
Menendez also stresses that getting a nuclear deal with North Korea will not be the hard point, noting that several previous presidents were able to strike deals only to see them fall apart. As a part of that process, he also announced a suspension of nuclear and missile tests and the dismantlement of a key atomic testing facility that was carried out last month.
Trump has arrived in Singapore — here’s what to expect tomorrow when he meets Kim Jong Un
President Trump is expected to meet separately with Singapore Prime Minister Lee Hsien Loong on Monday. Trump traveled to Singapore from Canada, where he attended a meeting with other world leaders.
"Substantive and detailed meetings in #Singapore today", Pompeo wrote on Twitter, along with photos of Sung Kim and North Korean officials at the negotiating table.
North Korea has so far presented Kim's sudden diplomatic overtures to his neighbors and to the United States as a logical next step following what Kim has claimed is the completion of his plan to develop a credible nuclear deterrent to what Pyongyang has long claimed is a policy of hostility and "nuclear blackmail" by Washington.
But critics have warned that the meeting risks being largely light on substance considering what is believed to be a wide gap between the US and the North on the denuclearization issue.
Mr Trump's comments, made shortly before his departure for Singapore, underline his recent efforts to curb expectations for the summit, the first between a sitting United States president and a North Korean leader. Francis said he wanted yet again to send "a special thought in friendship and prayer" to the beloved Korean people.
Travelling with him were top officials including Foreign Minister Ri Yong Ho, Defence Minister No Kwang Chol and Kim Yong Chol, a close aide of Kim who has been instrumental in the diplomacy that culminated in Tuesday's summit.
It's Kim's pursuit of nuclear weapons that gives his meeting with Trump such high stakes.
Trump told Lee that "we appreciate your hospitality and professionalism and your friendship".
It was not clear what Kim Jong Un, who arrived Sunday afternoon, was planning to do on Monday or whether he meant to leave his hotel, the St. Regis, about a half-mile from where Trump's delegation is staying.
The summit's venue is the Capella hotel on Sentosa, a resort island off Singapore's port with luxury hotels, a Universal Studios theme park and man-made beaches.
Many experts on North Korea, one of the most insular and unpredictable countries in the world, remain sceptical Kim will ever completely abandon its cherished nuclear weapons.