SINGAPORE -- U.S. President Donald Trump and North Korean leader Kim Jong Un on Tuesday signed an agreement after a brief one-on-one summit, expanded bilateral meeting and working lunch.
Toward the conclusion of the summit, Trump said, "The letter that we are signing is very comprehensive. And I think both sides will be very impressed with the result. A lot of goodwill went into this."
Kim told the assembled media "the world will see a major change."
Trump continued: "I would actually say that it worked out far better than anybody could have expected."
Neither Trump nor Kim would say what the agreement entails. However, when asked about the denuclearization of the Korean Peninsula, Trump told reporters, "We are starting that process very quickly, very very quickly, absolutely." He gave no other details.
While the two men were leaving a signing ceremony, a reporter asked Trump if the president would invite Kim to the White House. "Absolutely I will," he said.
Trump is to appear at a news conference later.
The day began just after 9 a.m. Singapore time, when Trump shook hands with Kim at the Capella Hotel, on the resort islet of Sentosa.
The handshake marked the first time for a sitting U.S. president to meet with a North Korean leader.
Trump and Kim later walked along a colonnade, inside the hotel and up a flight of stairs. At 9:06 a.m., they entered the room where they held their one-on-one meeting.
"I feel really great. It's gonna be a great discussion and I think tremendous success," said Trump. "I think it's gonna be really successful and I think we will have a terrific relationship I have no doubt."
"It was not easy to come here," said Kim. "We have the past which drags us back and such practices sometimes had blinded and deafened us. But we came to this place by overcoming all things."
The two leaders then went into a meeting with only translators.
When the session ended, Trump said the talk with Kim was "very, very good," according to AP. He also said he and Kim have an "excellent relationship."
Aids then joined at expanded meeting. "Working together we will get it taken care of," Trump said. "We will solve it...and I look forward to working on it with you. Thank you very much. Thank you very much, everybody."
"There will be challenges ahead but we will work with Trump," Kim said. "We overcame all kinds of skepticism and speculations about this summit, and I believe that this is good for peace."
The delegations at just past 11:30 moved to another room in the hotel for a working lunch.
The summit's outcome could prove pivotal in determining the course of denuclearization of the Korean Peninsula.
The key issue is North Korea's nuclear weapons program, which the U.S. wants dismantled in a complete, verifiable and irreversible manner. Pyongyang, however, is resistant to giving up an arsenal it has spent decades developing. Kim is likely to demand security guarantees for his regime as well as generous economic assistance.
Trump is to hold a press conference in the afternoon.
Key aides, including Secretary of State Mike Pompeo and Kim Yong Chol, vice chairman of the Workers' Party, are taking part. Pompeo and Kim Yong Chol ensured that the on-again, off-again summit would take place by flying to each other's capital in the past few weeks.
The summit has drawn global attention, especially in the stakeholder countries of South Korea, China and Japan.
South Korea, whose capital, Seoul, sits about 55km from the Demilitarized Zone, grew anxious last year as Trump and Kim traded not-so-veiled threats of nuclear war. China, stunned by the news of the summit, is nervous that Kim might turn toward the U.S. and Beijing would lose influence. Japan worries Trump will concede too much and that the delicate balance of power in the Asia-Pacific region could tilt China's way.
It was three months ago when South Korean mediators gave Trump word of Kim's request for a meeting. The U.S. president immediately said yes.
South Korean President Moon Jae-in, who played a significant role as a mediator, reacted to the start of the summit. In Seoul, he told his cabinet, "I really wish with our citizens that the meeting turns out to be successful, opening the door for complete denuclearization, peace and a new era among South Korea, North Korea and the U.S."
Moon also admitted that he "could not sleep well last night."
Masayuki Yuda contributed to this story.