At the summit held in Singapore yesterday, Trump and Kim signed a document in which North Korea committed to "complete denuclearisation of the Korean Peninsula" in exchange for US security guarantees.
Trump said Kim told him that he is getting rid of the nuclear weapons. "Yeah, he's de-nuking, I mean he's de-nuking the whole place. It's going to start very quickly. I think he's going to start now. They'll be announcing things over the next few days talking about other missile sites," the US president was quoted as saying by ABC News.
Trump said he also agreed to destroy a missile engine test site.
Trump said the US has assured security guarantee to the North Koreans.
"Well, we've given him (security guarantee), I don't want to talk about it specifically, but we have given him, he is going to be happy," he said.
Responding to a question, Trump said denuclearisation of Korean Peninsula does not mean that the nuclear umbrella that the US has over South Korea is on the table of negotiations.
Trump, however, said he did not discuss the withdrawal of US troops from South Korea with Kim.
"We didn't discuss that, no. But we're not gonna play the war games. You know, I wanted to stop the war games, I thought they were very provocative. But I also think they're very expensive," he said.
At his press conference in Singapore, Trump said that he would halt US military exercises in South Korea, something widely seen as a concession to Pyongyang as it has long claimed they are invasion rehearsals.
Describing the war games as very provocative and a drain on the economy, Trump has said that the US is not going to play war games: its military exercise with South Korea.
“I'm doing something that I've wanted to do from the beginning. We stopped playing those war games that cost us a fortune. You know, we're spending a fortune, every couple of months we're doing war games with South Korea, and I said, ‘What's this costing?' We're flying planes in from Guam, we're bombing empty mountains for practice,” Trump said.
“I said ‘I want to stop that and I will stop that, and I think it's very provocative,” he said.
Trump said he has invited Kim to the White House, but before the visit he wants to see some real progress.
"I want the process to start. I want to see some real work going on, which I believe I will, and I would love to have him at the White House whatever it takes, and I would love to have him at the White House, and I think he'd love to be there. And at a certain point when it's all complete I'd love to be there," he said.
"We are ready to write a new chapter between our nations," Trump told reporters after the much-talked about summit - the first between a sitting US president and North Korea's top leader.
Trump and Kim conducted a comprehensive, in-depth, and sincere exchange of opinions on the issues related to the establishment of new relations between the two countries and the building of a lasting and robust peace regime on the Korean Peninsula, according to a joint statement signed by Trump and Kim.