Singapore PM Lee Hsien Loong said that the joint statement "is a crucial first move in the long journey towards lasting peace and stability on a denuclearised Korean Peninsula, which would benefit our region and the rest of the world".
On nuclear weapons, Mr Kim "reaffirmed his firm and unwavering commitment to complete denuclearisation of the Korean peninsula".
But in an extraordinary media conference later, Mr Trump announced details are not in the paper.
South Korean President Moon Jae-In also unveiled a video produced for the North Korean leader during their meeting at the Demilitarized Zone in April.
"Yesterday's photo op doesn't change the fact that a nuclear-armed North Korea is a threat to the security of the United States, our allies, and the world".
Choi Seong-guk, who made cartoons depicting western spies, said: "What will make me angry [about the summit] will be seeing pictures of Kim parading around with global leaders".
Nice and handsome and thin and perfect
One of the four key points agreed to by President Trump and North Korean leader Kim Jong Un is to help repatriate the remains of Americans killed in action during the Korean War.
Asked if Kim had agreed to denuclearise, Trump said he expected the process to start "very, very quickly" and it would be verified by "having a lot of people in North Korea".
"It's going great. We had a really fantastic meeting", Trump said after the lunch.
However, the New Yorker noted that the brief agreement didn't meet standards previously sought by the US, in that North Korea's end of the bargain did not include that their denuclearization would be verifiable or irreversible. Although the United States and North Korea do not have formal diplomatic relations, all of the pageantry pointed to a meeting between near equals, a a masterful propaganda coup for the reclusive rogue state.
The working lunch was the final part of the summit between Trump and Kim.
Human rights abuses will be discussed eventually, she added, but the meeting between Trump and Kim should be seen as a step in the right direction.
Affirming that sanctions will stay in place until the North Korean nuclear capability is gone, Trump also answered several questions about the omission of the words "verifiable" and "irreversible" from the signed joint statement. Mr Trump said he wanted to see U.S. troops withdraw from the South.