But in an extraordinary media conference later, Mr Trump announced details not in the document. Trump grasped Kim's right arm as they shook, and then, later, took hold of Kim's left arm as they turned to face the cameras and the world, both their expressions momentarily deadening before they turned to face each other again, and smiled.
"The two top leaders gladly accepted each other's invitation, convinced that it would serve as another important occasion for improved DPRK-US relations".
Later Tuesday, Senate Minority Leader Chuck Schumer said, "We have legitimized a brutal dictator who has starved his own people".
The remarks were unusual for a US president.
He also expressed a desire to remove all 28,500 American troops stationed in South Korea, a pillar of U.S. engagement in Asia since the Korean War ended in 1953.
On Wednesday the foreign affairs minister, Julie Bishop, said the suspension of war games - a surprise concession offered by the USA president on Tuesday night that caught South Korea by surprise - was not in the official declaration but "the president spoke about it in answer to a question at a press conference". "We talk about unwavering commitment to the complete denuclearization of the Korean peninsula".
U.S. President Donald Trump and North Korea leader Kim Jong Un at the Capella resort on Sentosa Island Tuesday, June 12, 2018 in Singapore. The plan outlined in the two leaders' joint statement turns out to be exactly what Beijing wants. But the North has long sought an end to the USA military presence in the South, where Washington has around 28,000 troops stationed to protect it from its neighbour.
Both Seoul and U.S. military commanders in the South indicated they had no idea the announcement was coming, and analysts expressed immediate concern.More news: Kate Middleton takes George and Charlotte to watch William in polo match
The meeting was also a success from a security and optics points of view: smiles were exchanged, in-depth discussions took place between cabinet members, nobody went off script and there were no security breaches, thanks to ironclad preparations by their Singaporean hosts.
So, before I even ask you about the summit, what is this sort of after-the-summit set of statements say to you?
After the summit, Trump said the process of repatriating remains would begin immediately.
"We would like to seek an understanding of this between Japan, the United States and South Korea", Japan's defence minister, Itsunori Onodera, said.
"We will be stopping the war games, which will save us a tremendous amount of money", Mr Trump said, labelling the exercises "inappropriate" and "very provocative".
Trump praised Kim in an interview with ABC News after the summit where he stated, "His country does love him".
"Following this historic summit, I remain skeptical but hopeful that this new dialogue can translate into meaningful progress", Portman said in a statement. "I mean, they're going to be getting rid of sites". "That's going to start very soon". "It was a awful thing, it was brutal, but a lot of people started to focus on what was going on, including North Korea".