Trump said this in a telephonic conversation with the South Korean President Moon Jae-In during which the latter briefed him about his country's talks with the North Koreans.
"President Trump expressed his openness to holding talks between the United States and North Korea at the appropriate time, under the right circumstances," the White House said in a readout of the call.
Briefing reporters on his phone call, Trump said he had a good conversation with the South Korean leader.
"I just spoke to President Moon. He's very thankful for what we've done. They're having talks with North Korea. We'll see how that happens. He felt that the original -- that the initial talk was extremely good. Had a lot of good comment," he said during a Cabinet meeting at the White House.
"We had a very, very good conversation, and we'll see where it goes. He's very thankful for what we've done. It was so reported today that we were the ones -- without our attitude, that would have never happened. Who knows where it leads," he said.
"Hopefully, it will lead to success for the world -- not just for our country, but for the world. And we'll be seeing over the next number of weeks and months what happens," Trump said.
Moon also briefed Trump on his government's talks with a delegation from the North which resulted in Pyongyang agreeing to send a delegation to the Winter Olympics in Pyeongchang in South Korea next month, both sides said.
According to the White House, Vice President Mike Pence would lead the US delegation to the Winter Olympics.