Update, 4:10 a.m. EDT June 30: President Donald Trump and North Korean leader Kim Jong Un met for nearly after an hour after their historic handshake at the DMZ on Sunday. The two leaders agreed to restart talks again in an attempt to ease tensions between the two nations.
Trump said there was no timetable for another meeting with Kim.
"We're not looking for speed," Trump said. "We're looking to get it right."
Before he escorted Kim back to the border, the President said it was a monumental event.
"It was a great day. It was a legendary day," Trump said. "When I came into office, it was a fiery mess."
Trump also said he would extend at invitation to Kim to visit the United States "at the right time."
"We want to take it to the next step, and we'll see what happens," Trump said.
Update, 3:12 a.m. EDT June 30: President Donald Trump and North Korean leader Kim Jong Un met privately at the demilitarized zone after their historic handshake at the border between North Korea and South Korea.
Kim said his "excellent relationship" with President Donald Trump made their Sunday meeting at the DMZ possible.
"Just looking at this action, this is an expression of his willingness to eliminate all the unfortunate past and open a new future," Kim said.
North Korean leader Kim Jong Un said he and US President Donald Trump have an “excellent relationship."
"If it wasn't for that good relationship, we would not have been able to make this sudden meeting possible," Kim said, adding: “I had wanted to meet you again.”
"We met and liked each other from Day One," Trump said. "And that was important."
Update, 2:47 a.m. EDT June 30: President Donald Trump met North Korean leader Kim Jong Un at the DMZ on Sunday, and the president crossed over the border into North Korea, an unprecedented move.
"I feel great. It's a great honor to be here," Trump said. "Stepping across that line was a great honor. Progress has been made."
Kim also stepped across the border into South Korea.
Original report: Moon Jae-in, the South Korean president, announced that Kim accepted Trump's invitation to meet at the heavily fortified Korean border village of Panmunjom.
Moon praised Trump and Kim for "being so brave” to meet.
“I hope President Trump will go down in history as the president who achieves peace on Korean Peninsula,” Moon said.
Trump said the meeting would be "very short," but that it was a start.
“Virtually a handshake, but that’s OK," Trump said. "A handshake means a lot.”
"We have developed a very good relationship and we understand each other, I do believe he understands me and I think I maybe understand him and sometimes that can lead to very good things."
While in Japan, Trump said at a news conference that he was “literally visiting the DMZ,” but wasn’t sure whether Kim would meet him.
Trump’s summit with Kim in Vietnam earlier this year collapsed without an agreement for denuclearizing the Korean Peninsula. He became the first sitting U.S. president to meet with the leader of the isolated nation last year when they signed an agreement in Singapore to bring the North toward denuclearization.
The Associated Press contributed to this report.