WATCH: An historic handshake and meeting

President Donald Trump and North Korea's Kim Jong Un concluded an extraordinary nuclear summit Tuesday with the U.S. president pledging unspecified ``security guarantees'' to the North and Kim recommitting to the ``complete denuclearization of the Korean Peninsula.'' They coupled the summit agreement with lofty promises by Trump to handle ``a very dangerous problem'' and Kim's prediction for ``major change.''

Meeting with staged ceremony on a Singapore island, Trump and Kim came together for a summit that seemed unthinkable months ago, clasping hands in front of a row of alternating U.S. and North Korean flags, holding a one-on-one meeting, additional talks with advisers and a working lunch.

Both leaders expressed optimism throughout roughly five hours of talks.

Light on specifics, the document signed by the leaders largely amounted to an agreement to continue discussions as it echoed previous public statements and past commitments. It did not include an agreement to take steps toward ending the technical state of warfare between the U.S. and North Korea.

The pair promised in the document to ``build a lasting and stable peace regime'' on the Korean Peninsula and to repatriate remains of prisoners of war and those missing in action during the Korean War.

Language on North Korea's bombs was similar to what the leaders of North and South Korea came up with at their own summit in April. At the time, the Koreans faced criticism for essentially kicking the issue of North Korea's nuclear arsenal down the road to Tuesday's Trump-Kim summit. Trump and Kim even directly referenced the so-called Panmunjom Declaration, which contained a weak commitment to denuclearization and no specifics on how to achieve it.

The formal document signing followed a series of meetings at a luxury Singapore resort.

After the signing, Trump said he expected to ``meet many times'' in the future with Kim and, in response to questions, said he ``absolutely'' would invite Kim to the White House. For his part, Kim hailed the ``historic meeting'' and said they ``decided to leave the past behind.''

In a moment that would never happen in North Korea, reporters began yelling questions to Trump and Kim after they signed the document, including whether they had discussed the case of Otto Warmbier, the American college student who suffered brain damage while in North Korean custody and died in June 2017, days after he was returned home to Ohio.

The meeting was the first between a sitting U.S. president and a North Korean leader.

Aware that the eyes of the world were on a moment many people never expected to see, Kim said many of those watching would think it was a scene from a ``science fiction movie.''

After meeting privately and with aides, Trump and Kim moved into the luncheon at a long flower-bedecked table. As they entered, Trump injected some levity to the day's extraordinary events, saying: ``Getting a good picture everybody? So we look nice and handsome and thin? Perfect.''

Critics of the summit leapt at the leaders' handshake and the moonlight stroll Kim took Monday night along the glittering Singapore waterfront, saying it was further evidence that Trump was helping legitimize Kim on the world stage. Kim has been accused of horrific rights abuses against his people.

``It's a huge win for Kim Jong Un, who now, if nothing else, has the prestige and propaganda coup of meeting one on one with the president, while armed with a nuclear deterrent,'' said Michael Kovrig, a northeast Asia specialist at the International Crisis Group in Washington.

Trump responded to such commentary on Twitter, saying: ``The fact that I am having a meeting is a major loss for the U.S., say the haters & losers.'' But he added ``our hostages'' are back home and testing, research and launches have stopped.