But in an extraordinary media conference later, Mr Trump announced details not in the document.
Kim's vows to denuclearize were reported by state media Wednesday within that context - that Pyongyang would respond to easing of what it sees as the USA hostile policy against it with commensurate but gradual moves toward "the complete denuclearization of the Korean Peninsula".
In a post-summit interview with ABC News, the president said he was confident that the agreement meant full denuclearisation.
Ambassador Joseph DeTrani, who served as a top USA negotiator with Pyongyang before the last attempt at diplomacy broke down in 2009, was more optimistic.
At the truce village that divides the two Koreas, North Korean soldiers expressed enthusiasm for yesterday's Trump-Kim meeting.
Turnbull echoed that line: "I want to say that I do not believe that summit would have occurred had it not been for the absolute solidarity on the very tough economic sanctions on North Korea that have been imposed by the UN security council, that's had the support, obviously, of the United States and Japan and Australia and other countries, but also China".
This is certainly not the pledge for the unilateral dismantling of North Korea's nuclear programme that the USA has always pushed for. "There will be many more meetings, much more dialogue, a lot of diplomatic work to be done". -South Korea drills has been North Korea's "standard demand" for decades. Tuesday's statement made no mention of inspectors.
"If I have to say I'm sitting on a stage with Chairman Kim and that's going to get us to save 30 million lives, could be more than that, I'm willing to sit on the stage".
Democratic Senator Jeanne Shaheen said, "We can't lose sight of the fact that there are bad, horrific humanitarian issues in North Korea, human rights abuses". 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 news comes after the pair made history with a meeting in Singapore to try and bring an end to their differences. He even adopted North Korea's language for the exercises, calling them "very provocative".
"At best this is a tentative beginning down a road that will take many years, " he said by phone.
"I think he loved it", the president said.
"They weren't too excited about the summit".
Trump downplayed Beijing's role in the denuclearization process. "The two top leaders gladly accepted each other's invitation". Still, he offered no indication he planned to give up his arsenal, which he has called a "treasured sword".
It said the two countries would co-operate towards "new relations", while the U.S. would provide "security guarantees" to North Korea.
The meeting was the first between a sitting U.S. president and a North Korean leader.