Trump on Monday morning broke into a Twitter tirade about trade directed at America's European allies with the upbeat message: "Great to be in Singapore, excitement is in the air!".
"The entire world is watching the historic summit between (North Korea) and the United States of America, and thanks to your honest efforts. we were able to complete the preparations for the historic summit", Kim told Lee through an interpreter.
The leader's sister Kim Yo-jong is expected to be by her brother's side throughout the summit with U.S. President Donald Trump.
The meeting was Trump's only scheduled public event as White House officials prepared for the critical meeting on Tuesday with Kim.
Mr Kim has the "opportunity" to make a deal with the US, Mr Trump said on Saturday, but he "won't have that opportunity again".
Sanders says Trump spent his flight from Canada to Singapore "meeting with his staff, reading materials and preparing for his meetings in Singapore". USA ambassador to the Philippines, Sung Kim and North Korea's Vice Foreign Minister Choe Son-hui are expected to have a final coordination session, . following the six rounds of meetings they had in the inter-Korean village of Panmunjom to discuss the summit agenda.
Kim met the Singaporean prime minister, Lee Hsien Loong, briefly on Sunday, smiling broadly as the two posed for photographs.
After a flurry of contacts between the two Koreas, South Korean officials suggested to Trump in March that Kim would be willing to meet face-to-face.
One dispatch by the Korean Central News Agency said North Korea and the USA would exchange "wide-ranging and profound views" on establishing new relations, building a "permanent and durable peace-keeping mechanism", achieving denuclearization and "other issues of mutual concern, as required by the changed era".
Trump has arrived in Singapore — here’s what to expect tomorrow when he meets Kim Jong Un
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 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.
Last year, the North made one of the biggest breakthroughs in its missile and nuclear weapons programs - which it says it needs to defend against the risk of a USA invasion - when it announced that it had "completed" its state nuclear program after testing a missile capable of striking most, if not all, of the continental U.S.
Security around Kim's hotel was extremely tight and guests were prohibited from going in and out, hours before Kim's black Mercedes Benz limousine cruised in. But he also made clear Kim has a "one-time shot". It's a reflection of the intense global curiosity over Kim's sudden turn to diplomacy in recent months after a slew of North Korean nuclear and missile tests a year ago raised serious fears of war.
Before the negotiators' meeting on Monday, Pompeo had tweeted a photograph of himself and ambassador Kim, to show the United States position was unchanged: "We remain committed to the complete, verifiable, irreversible denuclearisation of the Korean Peninsula".
"Based on Justin's false statements at his news conference, and the fact that Canada is charging massive Tariffs to our U.S. farmers, workers and companies, I have instructed our U.S. Reps not to endorse the Communique as we look at Tariffs on automobiles flooding the U.S. Market!"
It's Kim's pursuit of nuclear weapons that gives his meeting with Trump such high stakes.
Kim had arrived hours earlier in a plane loaned by China, which for decades has been North Korea's only major ally.
Many remain sceptical Kim will ever completely abandon his nuclear programs.
Both the USA and North Korea have to agree on a venue that meets their requirements and is "politically and diplomatically" acceptable to them as well, he said.
Duke and Duchess of Sussex join Queen Elizabeth's birthday celebrations
The monarch is technically the head of Britain's armed forces and would traditionally lead an army into war. Royal blog Royal Central reports that this is the largest royal family gathering so far this year.