"Adversaries can indeed become friends," Trump said.
At the end of their historic meeting at the luxury Capella hotel on Singapore's Sentosa island, the first ever between leaders of the two nations, Trump and Kim signed an agreement to work toward complete denuclearization and a lasting "peace regime" on the Korean peninsula.
The document, which Trump deemed "very comprehensive," says the two sides commit to hold follow-up negotiations and to cooperate to develop bilateral relations.
Asked about what the agreement meant for North Korea's denuclearization, Trump said "we're starting that process very quickly — very, very quickly."
There was no mention of sanctions in the document, but Trump said after the summit those penalties on Pyongyang would remain in place until "the menace of nuclear weapons" is removed.
He also fended off questions about dealing with a dictator of a brutal regime in which dissent is not tolerated and opponents are killed.
"I think he liked me and I like him," Trump told Voice of America's Greta Van Susteren in an interview. "And I understand the past and, you know, nobody has to tell me, he's a rough guy. He has to be a rough guy or he has been a rough person. But we got along very well. He's smart, loves his people, he loves his country. He wants a lot of good things and that's why he's doing this."
Pressed by Van Susteren about human rights abuses, Trump said: "Look, he's doing what he's seen done, if you look at it. But, I really have to go by today and by yesterday and by a couple of weeks ago because that's really when this whole thing started. "
A photo of the document Trump signed revealed that the leaders of the United States and the Democratic People's Republic of Korea agreed on these four points:
1. The United States and the DPRK commit to establish new U.S.-DPRK relations in accordance with the desire of the peoples of the two countries for peace and prosperity.
2. The United States and the DPRK will join their efforts to build a lasting and stable peace regime on the Korean Peninsula.
3. Reaffirming the April 27, 2018 Panmunjom Declaration, the DPRK commits to work toward complete denuclearization of the Korean Peninsula.
4. The United States and the DPRK commit to recovering POW/MIA remains, including the immediate repatriation of those already identified.
In addition to those elements, the document says Trump "committed to provide security guarantees" to North Korea, an apparent reference to the authoritarian government's longstanding concern that the ultimate American goal is regime change in Pyongyang.
To follow up on the agreement, Secretary of State Mike Pompeo, national security advisor John Bolton and other members of the U.S. team will be "getting together" with North Korean officials next week to work out details of their agreement, Trump said. He added that he and Kim will "probably" need another meeting, but one hasn't been set.
"Mike, our whole team has to get to work and get it completed because, otherwise, we've done a good job, but if you don't get the ball over the goal line, it doesn't mean enough," Trump told his secretary of State at the conclusion of Tuesday's news conference.