U.S. 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."

Speaking at a news conference after the summit in Singapore, Trump said there's more to be done but "we're ready to write a new chapter between our nations." Talks will continue and Trump said he'd invite Kim "at the appropriate time" to come to the White House.

After the summit, Trump spoke for over an hour and said even he was surprised by how well it went.

"We're much further along than I would have thought," he said, crediting the preparation done by both sides in the weeks ahead of the summit, which included an apparent cancellation of the talks by the president.

For now, sanctions remain in place but Trump told reporters he looks forward to lifting them when "we are sure the nukes are no longer a factor."

He said "they want to make a deal, and making a deal is a great thing for the world."

Light on specifics, the document 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.

Trump says South Korea joint military exercises - war games - will be stopped as part of today’s agreement. “It’s very provocative,” and “we’ll save money... a lot!” says Trump <a href="https://twitter.com/hashtag/CBC?src=hash&ref_src=twsrc%5Etfw">#CBC</a> —@sasapetricic Trump says North Korea poor human rights record discussed “relatively briefly” in meeting with Kim Jong-un. “It’s rough,” he says. “But it’s rough in a lot of places” <a href="https://twitter.com/hashtag/CBC?src=hash&ref_src=twsrc%5Etfw">#CBC</a> —@sasapetricic

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.

'Bold step'

At the news conference, Trump said the pair spent "very intensive hours" together over the course of the day. He thanked Kim for taking what he called "the first bold step toward a bright new future for his people."

Trump said the meeting proves that "real change" is possible, and called the meeting "honest, direct and productive." He said that Kim also agreed to destroy a "major" missile testing site, but didn't offer details.

U.S. President Donald Trump holds up a document he and North Korea's leader Kim Jong-un signed following a signing ceremony during the historic summit, at the Capella Hotel on Sentosa island in Singapore on Tuesday. (Saul Loeb/AFP/Getty Images)

He also said the United States would stop engaging in joint military exercises with South Korea — which many analysts will view as a concession — unless it's proven that North Korea is contravening the spirit of the agreement.

U.S. political and military officials over the years have characterized the drills as routine, defensive and absolutely crucial, and it didn't appear they were on the table to negotiate in the weeks leading to Singapore.

There are 28,500 U.S. troops stationed in South Korea. Trump said the cessation of exercises would "save us a tremendous amount of money."

Lindsey Graham, South Carolina Republican who has occasionally been critical of Trump, told NBC's Today on Tuesday that he "violently" disagrees with removing troops from the Korean Peninsula.

Graham said the summit was a positive step forward but said Congress should vote on any agreement reached by the president.

While I am glad the president and Kim Jong-un were able to meet, it is difficult to determine what of concrete nature has occurred. - Bob Corker, Senate Republican

Also open to question was Trump's contention that Japan and South Korea are prepared to help North Korea economically but the U.S. "won't have to help them."

Bob Corker, the Republican chair of the Senate's foreign relations committee, was taking a wait-and-see approach.

"While I am glad the president and Kim Jong-un were able to meet, it is difficult to determine what of concrete nature has occurred," he said in a statement. "I look forward to having Secretary [of State Mike] Pompeo before our committee soon to share his insights and look forward to carrying out our oversight responsibilities."

The document signing and news conference followed a series of meetings at a luxury Singapore island resort.

Trump and Kim came together for a summit that seemed just 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.

Here’s the joint declaration signed by Trump and Kim <a href="https://t.co/OqvQsnfrf7">pic.twitter.com/OqvQsnfrf7</a> —@cbcsteve

Throughout the summit that could chart the course for historic peace or raise the spectre of a growing nuclear threat, both leaders expressed optimism. Kim called the sit-down a "good prelude for peace" and Trump pledged that "working together we will get it taken care of."

In advance of their private session, Trump predicted "tremendous success" while Kim said through an interpreter that "we have come here after overcoming" obstacles.

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."

American student's death not 'in vain': Trump

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."

Then they dined on beef short rib confit along with sweet and sour crispy pork.

U.S. President Donald Trump and North Korea leader Kim Jong-un walk from lunch at the Capella resort on Sentosa Island on Tuesday. (Susan Walsh/Associated Press)

And as they emerged from the meal for a brief stroll together, Trump appeared to delight in showing his North Korean counterpart the interior of "The Beast," the famed U.S. presidential limousine known for its high-tech fortifications.

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 as an equal of the U.S. president.

Trump has appeared largely unconcerned about the implications of feting an authoritarian leader suspected of ordering the public assassination of his half brother with a nerve agent, executing his uncle by firing squad and killing U.S. college student Otto Warmbier.

But Trump says without Warmbier's death, his meeting with Kim may not have happened. He says, "Otto did not die in vain."

Trump says human rights did come up during the talks, albeit briefly.

Trump said at his post-summit news conference that he understood the objections to meeting with Kim, but that he would "do whatever it takes to make the world a safer place."

The optimistic summit was a remarkable change in dynamics from less than a year ago, when Trump was threatening "fire and fury" against Kim, who in turn scorned the American president as a "mentally deranged U.S. dotard." Beyond the impact on both leaders' political fortunes, the summit could shape the fate of countless people — the citizens of impoverished North Korea, the tens of millions living in the shadow of the North's nuclear threat, and millions more worldwide.

Trump's motorcade travels towards Sentosa ahead of the summit, which began with a one-on-one meeting between the two leaders. (Feline Lim/Reuters)

It also capped a dizzying few days of foreign policy activity for Trump, who shocked U.S. allies over the weekend by using a meeting in Canada of the Group of Seven industrialized economies to alienate America's closest friends, with Trump lobbing insults on social media at his G7 host, Canadian Prime Minister Justin Trudeau.

Alluding to the North's concerns that giving up its nuclear weapons could surrender its primary deterrent to forced regime change, Pompeo told reporters that the U.S. was prepared to take action to provide North Korea with "sufficient certainty" that denuclearization "is not something that ends badly for them."

Experts believe the North is close to being able to target the entire U.S. mainland with its nuclear-armed missiles, and while there's deep skepticism that Kim will quickly give up those hard-won nukes, there's also some hope that diplomacy can replace the animosity between the U.S. and the North.

Yukiya Amano, head of the UN's International Atomic Energy Agency said the nuclear watchdog "stands ready to undertake any verification activities in [North Korea] that it may be requested to conduct by the countries concerned."