The US says its discussions with North Korea are moving "more quickly than expected" ahead of the summit in Singapore.
Preliminary talks between officials have been taking place ahead of the unprecedented first meeting.
The White House also confirms that US President Donald Trump and Kim Jong-un will hold a one-on-one meeting, with only translators present.
The outcome may determine the fate of North Korea's nuclear programme.
The US insists it will accept nothing less than complete denuclearisation of the Korean peninsula.
North Korea has said it is willing to commit to denuclearisation, but that term is open to interpretation.
It is also unclear what concessions Pyongyang could demand in return - which makes the summit very hard to predict, according to analysts.
Mr Kim has made a tour of some city sights, waving at spectators who cheered as he arrived to visit a high-end hotel.
Singapore's Foreign Minister Vivian Balakrishnan also tweeted a picture of them going "jalan-jalan", a local term meaning to go out for a walk, in the Gardens by the Bay park.
Mr Kim and Mr Trump are staying in separate hotels, not far from each other, and security is high across the area.
For decades, North Korea has been a pariah state, and now its latest hereditary leader is being treated as a world statesman.
Last year, it would have been a rare sight to see a North Korean flag flying anywhere in Asia. Now, Mr Kim - who runs a totalitarian regime with extreme censorship and forced-labour camps - is meeting and greeting dignitaries.
"The circus-like atmosphere might be amusing if the stakes weren't so high," wrote US campaigning group Human Rights Watch.
Mr Trump has said he has a "good feeling" about Tuesday's much-anticipated summit. Earlier in the day, he had lunch with Singapore's President Lee Hsien Loong and was presented with a cake ahead of his birthday on Thursday.
Former NBA star Dennis Rodman - one of the few Westerners to have met the North Korean leader on visits to the capital city of Pyongyang - is in Singapore.
He told reporters at Changi airport that he had come to Singapore "to see what's going on" and he hoped "that things turn out to be well for everyone in the world".
Mr Balakrishnan, who met Mr Trump and Mr Kim separately on Sunday evening, told the BBC that both leaders were feeling "supremely confident".
The two leaders will meet on Tuesday at a hotel on Sentosa, a popular tourist island a few hundred metres off the main island of Singapore.
According to the White House, the plan for the summit is that after initial greetings Mr Trump and Mr Kim will hold a one-on-one meeting, then an expanded meeting with other representatives before a working lunch.
There was speculation that the summit might continue into a second day, however Mr Trump is now scheduled to leave Singapore on Tuesday evening. Mr Kim is reported to be flying out even earlier, at 2pm local time.
Highly unusually, North Korea's state-run media are already reporting on Mr Kim's trip to Singapore to meet Mr Trump. As a rule, they would only report on the leader's movements after the event. An editorial in the Rodong Sinmun news outlet also talked about a "new relationship" with the US.
US Secretary of State Mike Pompeo said the president was fully prepared for the meeting. He said the US would be satisfied with nothing less than the complete, verifiable and irreversible denuclearisation of the Korean peninsula - with verification the key part of any deal.
The US was prepared to offer certainty to North Korea so it could be "comfortable that denuclearisation isn't something that ends badly for them". He would not be drawn on what might be on offer.
- BBC / Reuters