It added that denuclearization on the Korean peninsula would be dependent on the two sides "refraining from antagonizing... each other out of mutual understanding". They had a summit as a nuclear state with Kim on equal turf with Trump, got the United States to halt joint military exercises with South Korea.
The declaration took some South Korean and US military officials by surprise - though US Defence secretary Jim Mattis was not among them, with spokeswoman Dana White saying "there were no surprises". The drills help keep USA forces at a state of readiness in one of the world's most tense flashpoints.
He also said he wanted to bring United States troops home - although he did not specify a timeframe.
Trump's diplomacy "sends all the wrong messages to China, North Korea and Russian Federation", said Malcolm Davis, a senior analyst at the Australian Strategic Policy Institute.
He paused for a moment, then added: "I don't know that I'll ever admit that".
But Trump faced skepticism from Democrats and some Republicans, as well as former USA officials who warned of past empty pledges from North Korea.
A spokeswoman for USA military forces in Korea said it had not received any direction to cease joint military drills.
Kim Jong Un invited Donald Trump to visit North Korea during their historic summit and the US President accepted, Pyongyang state media reported Wednesday, calling it the start of a "radical switchover" in the nuclear-armed Cold War foes' fraught relations.
Trump later extolled the North Korea leader on Twitter, writing that "there is no limit to what NoKo can achieve when it gives up its nuclear weapons and embraces commerce & engagement w/ the world".
Brit Hume, a Fox News senior political analyst, said Monday it was "disconcerting" to see President Donald Trump shake hands with North Korean leader Kim Jong Un, whom he called a "thug".
Trump called the North Korean leader "worthy", "smart" and "talented" after the Singapore summit while days earlier describing Trudeau as "dishonest and weak" following a G7 summit in Quebec.
"We would like to seek an understanding of this between Japan, the USA and South Korea", Japan's defence minister, Itsunori Onodera, said.
Xi's pre-summit meetings with Kim helped restore ties that had been frosty since both leaders took power around the same time about six years ago.
In addition to his one-on-one with Trump, Kim also impressed observers in "four-by-four" talks, enlisting former spy chief Kim Yong-chol, Foreign Minister Ri Yong-ho and vice-chairman of the Workers' Party of Korea Ri Su-yong for discussions.
Trump's signature, which Leong said looked like "arrows or skyscrapers", points to people who "tend to wear a mask to hide their true nature".
Highlighting the continued differences in the two countries' views of the denuclearization process, the report also said that they had agreed on a "step-by-step" approach. "I mean, they're going to be getting rid of sites". "I think, honestly, [Kim] is going to do these things".