As the two leaders met, Singapore navy vessels, and air force Apache helicopters patrolled, while fighter jets and an Gulfstream 550 early warning aircraft circled.
Financial markets were largely steady in Asia and did not show any noticeable reaction to the start of the summit. The dollar was at a three-week high and the MSCI index of Asia-Pacific shares was largely unchanged from Monday.
While Trump and Kim search each other’s eyes and words for signs of trust or deceit, the rest of the world will be watching, hoping that somehow these two unpredictable leaders can find a way to defuse one of the planet's most dangerous flashpoints.
Body language expert said both men tried to project command as they met, but also displayed signs of nerves.
After the meetings, the two teams and other senior officials met for a working lunch, where beef short ribs, sweet and sour pork and "Daegu Jormin", or Korean braised cod, were served for the main course, according to the menu. That was to be followed by dark chocolate tarts, pastries and vanilla ice cream for dessert. The North Korean leader's sister and close confidante Kim Yo Jong was among the lunch party.
As the cameras captured the moment, Trump quipped: "Very nice. Getting a good picture everyone, so we all look nice and handsome and thin...perfect".
In the hours before the summit began, Trump expressed optimism about prospects for the first-ever meeting of sitting U.S. and North Korean leaders, while Pompeo injected a note of caution whether Kim would prove to be sincere about his willingness to denuclearise.
Pompeo 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.
North Korea, however, has shown little appetite for surrendering nuclear weapons it considers vital to the survival of Kim's dynastic rule.
Sanctions on North Korea would remain in place until that happened, Pompeo said on Monday. "If diplomacy does not move in the right direction ... those measures will increase."
The White House said later that discussions with North Korea had moved "more quickly than expected" and Trump would leave Singapore on Tuesday night after the summit, rather than Wednesday, as scheduled earlier.
Kim is due to leave on Tuesday afternoon, a source involved in the planning of his visit has said.
One of the world's most reclusive leaders, Kim visited Singapore's waterfront on Monday, smiling and waving to onlookers, adding to a more affable image that has emerged since his April summit with South Korean leader Moon Jae-in.
Trump spoke to Moon and Japan's Prime Minister Shinzo Abe, both key allies of Washington in the region, to discuss developments ahead of the summit.
"I too, got little sleep last night," Moon told his cabinet in Seoul as the summit began in Singapore.
"I truly hope it will be a successful summit that will open a new age for the two Koreas and the United States and bring us complete denuclearisation and peace."