U.S. Secretary of State Mike Pompeo said the preparatory talks were moving quite rapidly and "and we anticipate that they will come to their logical conclusion even more quickly than we anticipated."
The summit provides "an unprecedented opportunity to change the trajectory of our relationship and bring peace and prosperity" to North Korea, Pompeo told a news conference on the eve of the summit.
However, he played down the possibility of a quick breakthrough and said the summit should set the framework for "the hard work that will follow", insisting that North Korea had to move toward complete, verifiable and irreversible denuclearisation.
Sanctions on North Korea would remain in place until that had happened, Pompeo said. "If diplomacy does not move in the right direction...those measures will increase."
Kim and Trump arrived in tropical Singapore on Sunday for the first ever face-to-face meeting by leaders of two countries that have been enemies since the 1950-1953 Korean War.
Although gaps remain over what denuclearisation would entail, Trump sounded a positive note in a lunch meeting with Singapore's Prime Minister Lee Hsien Loong.
"We've got a very interesting meeting ... tomorrow, and I just think it's going to work out very nicely," Trump said.
Lobster bisque, beef tenderloin and ice cream were on the lunch menu, and there was also an early birthday cake for Trump, who turns 72 on Thursday.
Kim remained ensconced in the heavily guarded St Regis Hotel, where he is staying. There was also no sign of his sister, Kim Yo Jong, who has accompanied him to Singapore.
Some people were grumbling in the wealthy city-state because of traffic jams caused by the summit and the cost of hosting two leaders with massive security needs. Lee has said the summit would cost Singapore about S$20 million ($15 million), more than half of which would go on security.
"Thanks PM Lee for spending $20 million of taxpayers money, which can ... help a lot of needy families in Singapore to survive," posted one Facebook user. Others complained about the traffic jams in downtown Singapore.
Lee said the cost was worthwhile.
"It is our contribution to an international endeavour which is in our profound interest," he told reporters on Sunday.
Trump and Kim are staying in separate hotels in the famous Orchard Road area of Singapore, dotted with high-rise luxury apartment blocks, offices and glittering shopping malls. Traffic was held up in the steamy midday sun and scores of bystanders were penned in by police when Trump went to meet Lee.
Commenting for the first time on the summit, North Korea's state-run KCNA news agency earlier said the two sides would exchange "wide-ranging and profound views" to re-set relations. It heralded the summit as part of a "changed era".
Discussions would focus on "the issue of building a permanent and durable peace-keeping mechanism on the Korean peninsula, the issue of realising the denuclearisation of the Korean peninsula and other issues of mutual concern," KCNA said.
In the lead up to the summit, North Korea rejected any unilateral nuclear disarmament, and KCNA's reference to denuclearisation of the peninsula has historically meant that Pyongyang wants the United States to remove its "nuclear umbrella" protecting South Korea and Japan.
Many experts on North Korea, one of the most insular and unpredictable countries in the world, remain sceptical Kim will ever completely abandon nuclear weapons. They believe Kim's latest engagement is aimed at getting the United States to ease the crippling sanctions that have squeezed the impoverished country.
A Trump administration official, speaking on condition of anonymity, said the U.S. side was entering the talks with a sense of optimism and an equal dose of scepticism given North Korea's long history of developing nuclear weapons.
"We will not be surprised by any scenario," said the official.
The official said Trump and Kim would hold a one-on-one meeting on Tuesday that could last up to two hours. He described it as a "get to know you plus" meeting.
Later, they would be joined by their respective negotiating teams for discussions that could last another hour.
The summit's venue is the Capella hotel on Sentosa, a resort island off Singapore's port with luxury hotels, a Universal Studios theme park and man-made beaches.
Trump initially touted the potential for a grand bargain with North Korea to rid itself of a nuclear missile programme that has advanced rapidly to threaten the United States.
But he has since lowered expectations, backing away from an original demand for North Korea's swift denuclearisation.
He has said the talks would be more about starting a relationship with Kim for a negotiating process that would take more than one summit.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.