The US says its discussions with North Korea are moving "more quickly than expected" ahead of the summit in Singapore on Tuesday.
The preliminary talks between officials have been taking place ahead of the unprecedented first meeting.
The White House also confirms that President Donald Trump and Kim Jong-un will hold a one-to-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.
The night before the big day
As night closed in, Mr Kim made a tour of some city sights. He waved 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. Security is high across the area.
Why is this remarkable?
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 Balakrishnan, who met Mr Trump and Mr Kim separately on Sunday evening, told the BBC that both leaders were feeling "supremely confident".
Mr Trump has said he has a "good feeling" about Tuesday's much-anticipated summit.
Great to be in Singapore, excitement in the air!— Donald J. Trump (@realDonaldTrump) June 11, 2018
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.
What is the agenda?
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, this is the plan for the summit:
- Mr Trump and Mr Kim initial greetings (09:00 local time; 01:00 GMT)
- One-to-one meeting
- Expanded meeting with other representatives
- 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 14:00 local time.
What has North Korea said?
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.
What has the US said?
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.
How did we get here?
The two leaders have had an extraordinary up-and-down relationship over the past 18 months.
Mr Trump's first year in office was marked by bitter exchanges between himself and Mr Kim - as North Korea conducted several ballistic missile tests in defiance of the international community.
The US president successfully sought to tighten UN sanctions on the North, and to get its traditional ally, China, to go along.
He also famously vowed to unleash "fire and fury" if Pyongyang kept threatening the US. Mr Kim has called him "mentally deranged" and a "dotard".
A defiant North Korea carried out its sixth nuclear test in September 2017. Soon after, Mr Kim declared that his country had achieved its mission of becoming a nuclear state, with missiles that could reach the US.
In early 2018, a remarkable turnaround in the relationship occurred.
It started with significant diplomatic overtures from North Korea towards South Korea during the Winter Olympics. In March, Mr Trump shocked the world by accepting an invitation from Mr Kim to meet in person.