President Trump followed his historic meeting with North Korean leader Kim Jong Un with a press conference heralding a message of hope, vision and peace.

The president said 70 years after the Korean War began, the world entered a new chapter and a new history. He said vigorous negotiations would began immediately toward the complete denuclearization of North Korea and pledged they would stop war games. He indicated they would meet again to discuss Kim's commitment to denuclearization, saying they were "much further along" than he would have thought.

MORE: 'Anyone Can Make War, Only the Most Courageous Can Make Peace': Trump's Historic N Korea Agreement

North Korea, he said, has a "substantial arsenal" of nuclear weapons, adding that the summit should have taken place five years ago.

The two leaders signed an agreement "to build a lasting and stable peace regime." It also provides "security guarantees" by the US for North Korea.

With the entire world watching, they met on Tuesday at a hotel in Singapore in front of a display of American and North Korean flags to began their historic face-to-face summit over the fate of Pyongyang's nuclear arsenal and the prospect of peace between the two nations.

Speaking to reporters with Kim sitting by his side, Trump said: 'I feel really great we'll have a great discussion and I think a great success, tremendously successful. It's my honor. We'll have a tremendous relationship no doubt."

"The past was filled with obstacles and prejudices, but we got past them and we are here today," Kim responded through his interpreter.

At their farewell meeting, a reporter asked President Trump what surprised him most about the North Korean leader. He replied, "A great personality and very smart. Good combination. He's a worthy negotiator, negotiating on behalf of his people. A very worthy, a very smart negotiator. We had a terrific day. We learnt a lot about each other and about our countries. I learnt he is a very talented man. I also learned that he loves his country very much."

Another reporter asked the president if they would be meeting again. He replied, "We will meet again; we will meet many times."

They bid farewell and began a process many hope will lead to the denuclearization of the Korean Peninsula and even perhaps the end of the Korean War.

The meeting between the two leaders was billed by political experts as one of the most highly anticipated diplomatic meetings in the last century.

President Trump said Monday he would know if Kim was sincere about peace within the first couple of minutes of their meeting.

The schedule for the meeting had been set for several days. When he emerged from his one-on-one talk with Kim, Trump said the meeting was "very, very good" and that the two have an "excellent relationship."

Trump and Kim talked for about 40 minutes with only interpreters present in the room.

The president made the comments while he and Kim walked together as they headed to a larger meeting with their aides.

Trump was joined by White House Chief of Staff John Kelly, Secretary of State Mike Pompeo and National Security Advisor John Bolton. The four men sat across the table from Kim and his team.

After the larger meeting, the group will then transition to a working lunch.

Up early in preparation for the meeting Tuesday morning, Trump tweeted, "Meetings between staffs and representatives are going well and quickly ... but in the end, that doesn't matter. We will all know soon whether or not a real deal, unlike those of the past, can happen!"

US officials have said a best-case scenario would be that the summit serves as the platform for further negotiations, providing Kim and his heavily sanctioned nation with economic guarantees in exchange for dismantling his country's nuclear capabilities once and for all.

"I believe we're going to have a terrific success or a modified success," Trump said during a press conference last week with Japanese Prime Minister Shinzo Abe. "But I really believe that we have the potential to do something incredible for the world. And it's my honor to be involved."

Secretary of State Mike Pompeo tried to keep expectations about the talks in check.

"We are hopeful this summit will have set the conditions for future successful talks," Pompeo said.

Trump will have only a few hours with Kim as the White House announced the president would be leaving Singapore on Tuesday evening. The White House said Trump was leaving early because negotiations had moved "more quickly than expected," but gave no details.

Following the meeting, Trump will hold a press conference with reporters as Kim departs for North Korea.

The president plans to stop in Guam and Hawaii on his way back to Washington.

On Monday, US and North Korean officials met at a Singapore hotel working out last minute details and trying to get acquainted after years of little to no contact between the two governments.

Trump spoke only briefly in public Monday predicting a "nice" outcome.

It is not known if the president will bring up the issue of human rights at the meeting. Just hours before meeting with Kim, the president took to Twitter to lash out at his critics.

"The fact that I am having a meeting is a major loss for the US, say the haters & losers," Trump wrote. "We have our hostages, testing, research and all missile launches have stopped, and these pundits, who have called me wrong from the beginning, have nothing else they can say! We will be fine!

The fact that I am having a meeting is a major loss for the U.S., say the haters & losers. We have our hostages, testing, research and all missle launches have stoped, and these pundits, who have called me wrong from the beginning, have nothing else they can say! We will be fine! — Donald J. Trump (@realDonaldTrump) June 11, 2018

Kim, 36, now finds himself on the world stage dealing with the president of the United States. Even though the negotiations could mean even more politically for both men, it could mean perhaps even more for the poverty-stricken citizens of North Korea.

Just about a year ago, Trump and Kim were trading insults. The president was threatening "fire and fury" against Kim, who called Trump "a "mentally deranged US dotard."