The jet carrying Kim landed at the airport Sunday afternoon amid huge security precautions on this city-state island.
Kim's private plane did travel to Singapore, but is believed to have carried sister Kim Yo Jong and other top-ranking members of the delegation.
Pompeo had earlier tweeted a photograph at breakfast with ambassador Kim, stating the USA position was unchanged: "We remain committed to the complete, verifiable, irreversible denuclearization of the Korean Peninsula".
Kim arrived Sunday at the St. Regis hotel, where his close aide has been based as he leads a North Korean advance team arranging security and logistics details.
Donald Trump has sat down for lunch with his Singapore's Prime Minister Lee Hsien Loong.
US President Donald Trump, left, shakes hands with Singapore's Prime Minister Lee Hsien Loong during his visit to The Istana, the official residence of the prime minister, in Singapore on June 11, 2018.
Kim arrived Sunday on a Chinese plane, not his official plane, which is called "Chammae-1" and named after the goshawk, North Korea's national bird.
The North has presented Kim's sudden diplomatic overtures to the country's neighbours and the U.S. as a logical next step and completion of his plan to develop a credible nuclear deterrent in response to what Pyongyang says is a policy of "nuclear blackmail" by Washington. Pyongyang has accused the USA and South Korea of plotting to kill Kim with chemical weapons in the past, and China is rumored to have explored an assassination plot involving his half-brother, Kim Jong Nam.
Trump also spoke by telephone on Monday with South Korean President Moon Jae-in, according to officials in Seoul who predicted that if Tuesday's Singapore summit is a success it would be a "gift" to the entire world.
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The young woman talked the restricted lifestyle of North Koreans and public executions that follow in case the rules are broken. Kim has led the USA team at the demilitarized zone working on a joint communique with North Korea.
North Korea has repeatedly expressed a commitment to the "denuclearisation of the Korean peninsula" - notably in a report by state agency KCNA on the eve of the summit - but the term is open to interpretation on both sides and it remains unclear what concessions Kim is prepared to offer.
The story was reported the front page of the ruling party's newspaper and was the only item on Monday's first news broadcast on Korean Central Television, which for many in the North is the only channel available.
Trump hopes the landmark talks will kick-start a process that eventually see Kim give up his nuclear weapons in an irreversible manner that can be verified internationally. The session will be expanded to a bilateral meeting and will include advisors. The US president has also raised the possibility of further summits and an agreement ending the Korean War by replacing the armistice signed in 1953 with a peace treaty.
North Korea once enjoyed two sponsors, China and the Soviet Union.
Pompeo said these guarantees would be "different and unique" from what the USA has been willing to provide before.
The short answer might be that, despite his safety worries, Kim could end up getting much more out of this summit than he will have to give up.
Singapore is one of the few countries that have diplomatic relations with both the U.S. and North Korea. "[North Korea's] media is old school", explained North Korea expert and journalist Jean Lee in a tweet.
Speaking ahead of Tuesday's US-North Korea summit in Singapore, Mr Pompeo said preliminary talks between senior officials were continuing and moving quite rapidly.
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