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.
The Trump administration seeks a "complete, verifiable and irreversible" dismantlement of Pyongyang's vast nuclear weapons program, which has produced up to 60 nuclear warheads housed across the country, according to United States intelligence estimates, as well as a sophisticated program for their delivery worldwide.
"We signed a very comprehensive document and I think he's going to live up to that", Trump said, adding that there would be "vigorous negotiations as soon as possible".
"I think over the weeks that they spent with us, they gained greater confidence that we are sort of no-nonsense but efficient people", he said.
Kim hailed the day's discussions as "historic".
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 unsafe flashpoints.
Trump did not refer to the document as a treaty or agreement.
"The world will see a major change", the North Korean leader said.
"We sat down for lunch", Rodman said of a face-to-face meeting with Kim five years ago.
"They may be able to pull rabbits out of a hat that the rest of us conventional diplomats would not have been able to do", he said. "It worked out for both of us far better than anybody could've expected, far better than even anybody would've even predicted".
It is that delivery system, in the form of intercontinental ballistic missiles, that prompted the most crisis between Washington and Pyongyang and led Trump to threaten a new armed conflict.
"Rather than signing an unsubstantial agreement, Trump and Kim should be signing a real document based on worldwide law, the Treaty on the Prohibition of Nuclear Weapons". "Very very quickly", he said, without elaboration. However, others reported that the Air China Boeing 747 took off before the leader's jet did by an hour or two as a security measure to avoid making his mode of transportation known.
"Nice to meet you, Mr. President", Kim was overheard telling Trump.
Though small, Singapore is also wealthy, and able to shoulder the cost of the historic summit, which would appeal to cash-strapped North Korea. According to Reuters, earlier this month Singapore's Defense Minister Ng Eng commented on Singapore paying for numerous expenses of the sit down between Trump and Kim. He said he would discuss it "at great length" at an upcoming news conference, and indicated it would be made available publicly. "It's my honor, and we're going to have a terrific relationship".