"A long trip, but everybody can now feel much safer than the day I took office", Trump simpered.
"There is no longer a Nuclear Threat from North Korea".
Japan has maintained a hardline position on North Korea despite a whirlwind of diplomacy towards Pyongyang in recent months, and has been left largely on the sidelines as South Korea and the United States have held talks with Kim.
But he said that was no longer the case, and everyone can "sleep well tonight".
At a news conference in Singapore after almost five hours of talks there with Kim, Trump said he "knows for a fact" that North Korea is serious about denuclearization this time and that Kim "wants to do the right thing".
VideoNorth Korean leader Kim Jong-un and US President Donald Trump sign a document after their summit.
The Japanese government has officially listed 17 people as abductees, but there are strong suspicions that dozens more citizens were snatched to train Pyongyang's spies in the Japanese language and culture.
"I do trust him, yeah", Trump said. It's unclear whether the president informed USA allies in the region of his plan to end the "war games", as he called them, prior to his declaration.
The state media said talks were "epoch making" and would help to kickstart a "radical switchover in the most hostile [North Korea]-US relations".
North Korean state media lauded the summit as a resounding success, highlighting concessions made by the U.S. president.
The top United States diplomat was in South Korea to brief officials on the summit before traveling to China, where he will offer further briefings on the summit and regional issues with leaders there.
Trump and Kim Jong Un have now parted ways, since Singapore is 12 hours ahead of Eastern Daylight Time, and are heading home, but here's a round up of the biggest moments from their time together.
The article also states that Trump accepted Kim's invitation to visit Pyongyang, while Kim accepted an invitation from Trump to visit the US.
In Pyongyang, North Korean state media heralded claims of a victorious meeting with the USA president; photos of him standing side-by-side with Trump on the world stage were splashed across newspapers.
For weeks, Pompeo and other officials have insisted North Korea must agree to "complete, verifiable, irreversible denuclearization" before economic sanctions can be lifted.
The pair are set to meet until early afternoon, when it is hoped that they will present a joint agreement including steps for the North's abandonment of nuclear weapons.
"So I reject that analysis that it costs too much, but I do accept the proposition, let's stand down [on military exercises] and see if we can find a better way here". Trump later interacted with media persons from across the world covering the event. "They are fighting hard to downplay the deal with North Korea".
Current and former U.S. defence officials expressed concern at the possibility that the United States would unilaterally halt military exercises without an explicit concession from North Korea that lowers the threat from Pyongyang.
Kim spoke at the signing, through a translator, saying that they had a "historic meeting and chose to leave the past behind". And it says they will commit to recovering the remains of prisoners of war and those missing in action.