Speaking to reporters outside the White House, Trump said president Barack Obama told him before he took office that the "most dangerous problem" for the United States was North Korea's nuclear weapons program.
"I have solved that problem," Trump said. "Now we're getting it memorialized and all but that problem is largely solved."
"We signed a very good document," he said.
"But more importantly than the document, I have a good relationship with Kim Jong Un," he said, adding that they have "great chemistry together."
"That's a very important thing," he said. "I can now call him.
"I gave him a very direct number. He can now call me if he has any difficulty. We have communication."
"People are shocked," the president continued. "They thought Trump was going to get in, he's going to start throwing bombs all over the place.
"It's actually the opposite."
Trump said there would be a "very strong verification process" for North Korean denuclearization.
"We're well on our way to getting denuclearization, and the agreement says there will be total denuclearization," he said.
'War games'
Asked about North Korean human rights abuses, Trump said "I can't speak to that.
"I can only speak to the fact that we signed an incredible agreement, it's great and it's going to be great for them too because now North Korea can develop and North Korea can become a great country economically," he said.
"It can become whatever they want but there won't be nuclear weapons, and they won't be aimed at you and your family.
"Because I don't want to see a nuclear weapon destroy your family," he said.
"When I came in, people thought we were probably going to war with North Korea," he said. "If we did, millions of people would have been killed."
Trump defended his decision to unilaterally halt joint military exercises with South Korea.
"That was my offer. I call them war games," he said. "I hated them from the day I came in.
"We pay for it. We pay millions and millions of dollars for planes and all of this.
"I said I'd like to halt it because it's bad to be negotiating and doing it," he said. "I saved us a lot of money. That's a good thing for us."
Trump also said he would like Americans to "sit up at attention" when he speaks like North Koreans do for Kim.
"Hey, he is the head of a country and I mean he is the strong head," the president said. "Don't let anyone think anything different.
"He speaks and his people sit up at attention. I want my people to do the same," he said.
Trump later said he was kidding and that reporters "don't understand sarcasm."
Eyewitness? Submit your stories now via social or:
Email: eyewitness@pulse.ng
![Fiona Beal killed her partner and lied to everyone about what happened to him [Northamptonshire Police]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'300'%20height%3D'172'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "Fiona Beal killed her partner and lied to everyone about what happened to him [Northamptonshire Police]")
