Trump and Kim will meet on Tuesday at 9 a.m. for talks on denuclearization.
"Great to be in Singapore, excitement in the air!"
"Maybe we'll start with the White House, what do you think?" he said when asked if Kim would be invited to Washington or his Mar-a-Lago estate in Florida.
Brad Adams, Asia director at Human Rights Watch, said it was imperative that Trump bring up rights issues with Kim.
The path to economic reform and a better life for the people in North Korea is normalization of relations with the U.S. This has been a goal of Kim Jung Un and his father, Kim Jong il, but only on North Korea's terms: Accepting North Korea as a nuclear weapons state. Kim, who is showing increasing strategic sophistication on the other hand, is likely to be sharply focused on the details since his nuclear arsenal is seen in Pyongyang as the guarantor of his dynastic rule.
Kim smiled broadly in the meeting Sunday evening.
Lee is due to met Kim later on Sunday and Trump on Monday.
During a brief photo opportunity, Trump praised the professionalism of his Singapore hosts.
Kim Yo Jong, leader Kim's younger sister, was also spotted in his delegation.
Before Monday, official news outlets had reported only that the two leaders planned to meet, without saying where or when or offering any other specifics.
Since Kim chose to reach out through diplomatic means to the South in January of this year, he has signaled that he is prepared to accept certain aspects of the US-South Korea military alliance.
Both Kim and Trump have a strong incentive to declare the summit a success whatever happens.
Menendez spoke Sunday on ABC's "This Week" as President Donald Trump arrived in Singapore ahead of Tuesday's talks with Kim.
Kim may have shipped over the massive bulletproof and fireproof limousine that became a social media sensation when Kim was shown being driven across the border between the Koreas during his first summit with South Korean President Moon Jae-in, in April, with a dozen staunch bodyguards encircling the auto.
Trump and Kim landed in a city teeming with media and onlookers of all stripes, from foreign policy analysts like Kelly and Enos to former basketball star Dennis Rodman, who claims to be a friend of the two leaders.
"This is a leader who really is an unknown personality", Trump added of Kim. The North has faced crippling diplomatic and economic sanctions as it has advanced development of its nuclear and ballistic missile programs. The American president has expressed confidence that Kim will take him up on this "one-shot opportunity" to help improve North Korea's standard of living.
This is a thinly-veiled threat that Trump could simply deliver an ultimatum to Kim and then walk out if the latter does not fully accede to United States demands. And Trump is the first US president willing to sit-down with Kim with so few concessions, believing his self-professed negotiating prowess will guide him though uncharted diplomatic waters.
"To the extent that Kim Jong Un has already gone from global pariah to being normalized internationally, you have to say that he's had some success here", Menendez said.
"Otherwise", Drezner said, "he'll be 0-for-2 on this trip". Bolton has been far less visible in the planning process, after a comment he made about favoring the "Libya model" for denuclearization enraged the North Koreans.
"We have a chance to achieve a truly wonderful result for North Korea and the World", Trump posted on Twitter en route Singapore from Quebec, Canada, where he attended the G-7 summit.