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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-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.
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 a high across the area.
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.
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.
Mr Balakrishnan confirmed that Singapore was paying for the North Korean delegation's stay, describing it as "hospitality that we would have offered".
According to the White House, this is the plan for the summit:
Mr Trump will leave the country that same evening to return to the US.
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.
Mike Pompeo, Donald Trump's top diplomat, 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.
Analysis: Laura Bicker, BBC News, Singapore
For decades the US has been North Korea's sworn enemy. There are even anti-American museums in Pyongyang.
But the state is now trying to sell the idea of talking to what it once described as "the incarnation of all sorts of evil, the empire of devils". And that was some of its milder language.
In state news outlet Rodong Sinmun, an English-language editorial sells the summit as a chance to realise "the denuclearisation of the Korean peninsula and other issues of mutual concern, as required by the changed era".
It's the "changed era" that is important. North Korea has spent decades building up a nuclear arsenal at great cost. Kim Jong-un needs to tell his people why he's willing to negotiate.
His New Year speech - the one that kick-started this diplomatic process - was all about North Korea's strategy of building the economy, having achieved the goal of becoming a nuclear power. This has echoes of that.
These pages in the paper are significant because they pave the way for a possible change in the state's message and it helps those watching argue that this time with North Korea, things could be different.
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.
