WATCH: Videos of Trump & Kim Jong Un Singapore Summit

President Trump is declaring the historic Singapore summit a success after meeting with North Korean leader Kim Jong-un early Tuesday. According to CBS News, Trump and Kim were able to come to an understanding that “Pyongyang would work toward denuclearization and the United States would end joint military exercises with South Korea.” Trump and Kim both signed a document agreeing to a handful of key provisions, CBS reports.

According to the New York Times, “the two leaders first met privately for less than an hour in a one-on-one session with interpreters present, before breaking off for a larger meeting and then a working lunch with aides.”

Trump said at a news conference that the United States would stop “the war games,” and that the exercises were expensive and “very provocative.” In their joint statement, the United States “committed to provide security guarantees.” In exchange, Kim “reaffirmed his firm and unwavering commitment to complete denuclearization of the Korean Peninsula.”

“We had a historic meeting and decided to leave the past behind,” Kim said as he and Trump signed the joint statement, adding, “The world will see a major change.”

Trump was also optimistic about the progress they achieved, stating, “We are going to take care of a very big and very dangerous problem for the world.”

However, CBS reports that the United States and North Korea did not reach any specific agreement on how North Korea will achieve denuclearization. In a rare news conference after the summit, Trump stated that the U.S. will be “verifying,” that North Korea follows through. Check out video of the news conference below.

“Mr. Trump said the U.S. will be continuing sanctions until denuclearization occurs — but suggested sanctions might be lifted earlier than many experts thought possible,” CBS reports.

Trump claimed that the summit went “better than anybody would have expected,” that Kim had a great personality, and that he looked forward to inviting Kim to the White House.

“The old prejudices and practices worked as obstacles on our way forward, but we overcame all of it and we are here today,” Kim said after the summit.

President Trump stated that the death of Otto Warmbier, an American college student who was detained in North Korea, helped precipitate the meeting between the U.S. and North Korea, the president said Tuesday at a post-summit meeting news conference.

“I think without Otto this would not have happened,” Mr. Trump said. “Otto was someone who did not die in vain.”

The joint statement that both leaders signed said the two nations would hold “follow-on negotiations” between Secretary of State Mike Pompeo and a high-level North Korean official “at the earliest possible date, to implement the outcomes” of the summit meeting.

The statement also said that the two nations would “join their efforts to build a lasting and stable peace regime” on the Korean Peninsula, meaning “talks to reduce military tensions that could eventually lead to a formal peace treaty to end the Korean War,” according to the New York Times.

This is a developing story. Heavy will update as more information is released.