His remarks come days after his first and historic encounter in Singapore with the leader of the reclusive state on Tuesday.

Trump also said he plans to personally call Kim on Sunday.

"I'm going to speak to people in North Korea, and I'm going to speak to my people who are over in North Korea," he said.

Trump and Kim declared in a joint text following the summit their commitment toward complete denuclearization of the Korean Peninsula while guaranteeing the security of Kim's dynastic regime.

Regarding the summit outcome, Trump highlighted that he got "everything" in the deal and has "largely solved" North Korea's nuclear problem, in an apparent bid to spurn worries raised among Democrats that his encounter with Kim lacked details as to how to remove its nuclear and missile programs advanced enough to reach the United States.

"I have solved that problem ... that problem is largely solved," he said.

Trump also defended his decision not to press Kim during the summit over Pyongyang's human rights abuses, arguing that he did so because preventing a nuclear war is a more pressing matter.

It was his decision, Trump said, to suspend joint military exercises between South Korea and the United States, which North Korea has long condemned as an invasion rehearsal.

"That was my offer. Just so you understand," he said. "I call them 'war games.' I hated them from the day I came in ... We pay millions and millions of dollars for planes, and all of this."

He argued he was saving a lot of money by stopping the exercises. North Korea also refers to them as "war games," but Trump insisted it was his term.

He added that North Korea has begun returning the remains of US soldiers missing during the 1950-53 Korean War, which was part of their Singapore agreement.

"They are already starting to produce the remains of these great young soldiers," he said.

Nearly 1.8 million American troops participated in the 1950-53 conflict. Of them, 33,686 were killed and 3,737 went missing.

"We got along very well. We had a good chemistry," Trump said of his meeting with Kim in an interview with Fox News.

On whether Kim could be invited to the White House, Trump said he was open to the idea.

"I think it's something that could happen," he said. "Hey, he's the head of a country. And I mean he is the strong head. Don't let anyone think anything different. He speaks and his people sit up at attention. I want my people to do the same."

When a reporter at the White House later asked him to clarify, Trump replied, "I'm kidding. You don't understand sarcasm."

The president also spoke in the interview about the economic sanctions on Pyongyang, which were ramped up last year in response to North Korea's testing of intercontinental ballistic missiles and its sixth nuclear weapons test.

The sanctions won't be coming off until "we can be sure there will be no more nuclear," he said. Pressed on how close North Korea is to that stage, he added, "very close."

"We're very close to getting it started," Trump said.

In his remarks to reporters, he said without elaborating that there will be a "very strong" verification process in place. And he added his administration was "working it as fast as possible" to achieve denuclearization of the North.

 The president took pains to defend himself from criticism that the agreement was too weak and that he had given Kim the legitimacy he sought by simply meeting with him. No other sitting American president before Trump had met with a North Korean leader.

"I think it's great to give him credibility," he said. "Here's what we got, everything, point after point after point." (Yonhap)