Pompeo said he was "very optimistic" the meeting would be a success but played down chances of an immediate breakthrough, framing discussions as the start of a process.
Trump was expected to initially meet with Kim alone today, except for interpreters, to discuss the possibility of denuclearisation on the Korean Peninsula.
The US President said over the weekend he would know within a minute whether the North Korean leader was serious about giving up his nuclear arsenal.
The summit is a moment of history - the first time sitting leaders from both countries have ever met - and a remarkable turnaround from last year, when the pair were trading insults and threats.
After one-on-one talks, a wider bilateral meeting with senior advisers from both sides was planned to take place, followed by a working lunch.
The talks are being hosted at the luxury Capella hotel on Sentosa Island - just off the coast of Singapore - and are expected to last much of the day.
They are the culmination of weeks of scrambled backroom negotiations, and one public cancellation, after Trump accepted an unexpected offer from Kim to meet earlier this year.
THE TIMETABLE
1pm NZT Trump and Kim meet
1.15pm The two meet with translators
2pm Expanded meeting with representatives
3.30pm Working lunch
6pm Kim to leave
Midnight Trump to leave
Speaking yesterday, Pompeo gave the clearest outline yet of America's position as he described the incentives and warnings Trump would deliver to Kim.
"The complete, verifiable and irreversible denuclearisation of the Korean Peninsula is the only outcome that the United States will accept," he said.
"Sanctions will remain until North Korea completely and verifiably eliminates its weapons of mass destruction programmes.
"If diplomacy does not move in the right direction - and we are hopeful today it will continue to do so - those measures will increase."
But Pompeo added: "President Trump recognises Chairman Kim's desire for security and is prepared to ensure that a North Korea free of weapons of mass destruction is also a secure North Korea.
"The President's also expressed his openness to expanding access to foreign investment and other economic opportunities for North Korea if they take the right steps."
Pushed on what reassurances Kim would be offered over his security, Pompeo declined to give specifics but said the offers would be "unique" and "different" from those in the past.
He added that the Trump Administration wanted to show the North Koreans that denuclearisation "isn't something that ends badly for them".
Pompeo said the summit was "truly a mission of peace" and rejected claims that the Trump administration did not have enough nuclear scientists to oversee denuclearisation.
Asked whether America would offer to reduce the number of US troops stationed in South Korea - currently 28,000 - he declined to comment.
US and North Korean officials held negotiations in Singapore in a bid to close the gap between both sides. A White House spokesman said the talks had "moved more quickly than expected".
America wants sanctions to be lifted only once North Korea fully denclearises, while Kim's officials have voiced a preference for benefits to be phased in.
Trump, who Pompeo insisted is fully prepared for the meeting, tweeted yesterday: "Great to be in Singapore, excitement in the air!"
He met the Singaporean Prime Minister Lee Hsien Loong, thanking his "professionalism" over the summit's planning and expressing hope things could "work out very nicely". Trump also visited the US embassy.
Kim, who like Trump flew into the city-state on Sunday, was not seen for much of the day but his motorcade was spotted out in the city.
The North Korean leader had arrived on a Chinese plane rather than his own in a sign that the two countries' historic alliance remains intact.
As well as bringing his own limousine and food, Kim was reported to have brought his own portaloo to avoid his excretions being analysed for insights into his health.
Some 5000 journalists from across the world have gathered in Singapore for the summit. Trump is expected to fly home late tonight rather than staying another night.
North Korean state news announced the meeting - the first time the country's people had been told Kim's summit with Trump was definitely going ahead.
KCNA, the North Korean state media outlet, said that a "permanent and durable peace-keeping mechanism on the Korean Peninsula" would be discussed.
