Mr. Kim “might want to do this as much, or even more, than me,” Mr. Trump said. “I know when someone wants to deal and when they don’t.”

Even so, Mr. Trump added a note of caution: “I may be wrong. I may stand before you six months from now and say, ‘Hey, I was wrong.’”

Some of the biggest developments weren’t in the document signed by the two leaders. Mr. Trump said he would cease “tremendously expensive” and “provocative” joint military exercises with South Korea as long as productive talks continue with the North, a move he thought Mr. Kim would welcome.

Mr. Trump said that reducing the number of U.S. forces in South Korea isn’t part of the negotiation, but that he would eventually like to bring home the 28,500 U.S. troops based in South Korea to save money.

The U.S. has steadfastly refused to suspend joint military exercises in the past despite North Korean demands, and the pledge to do so is likely to unsettle Asian allies, who appeared to be taken by surprise by Mr. Trump’s statements. The Pentagon has long argued that the maneuvers, which it says are defensive in nature, are necessary to maintain the readiness of U.S. forces in South Korea.

South Korea’s Defense Ministry said it was trying to determine the meaning of Mr. Trump’s remarks, and a senior South Korean national-security official said “nothing has changed” on the exercises. A spokesman for U.S. Forces Korea said that it had received no new guidance on joint military maneuvers, including drills planned for the fall.

The decision came as a surprise to U.S. military officers in South Korea, who were “at a loss” about what would happen next, and whether there would be a cancelation of training with the South Korean military, according to a person familiar with the matter.

U.S. and South Korean forces recently completed an ambitious series of exercises, including the Foal Eagle annual maneuvers and Max Thunder, an air drill that drew North Korean protests. The only recent concession to Pyongyang’s sensitivities was a U.S. move to shelve a training exercise with the South Korea air force involving U.S. B-52s, which was made at Seoul’s request.

In addition, Mr. Trump said Tuesday that Mr. Kim had agreed to destroy a missile-engine testing site in a concession that wasn’t part of the written agreement. Mr. Trump’s remark was likely a reference to a missile test stand in the country’s northwest that North Korea had recently razed but not announced, which 38 North, a website on North Korean affairs, said last week Pyongyang had destroyed. In the report, analyst Joseph Bermudez pointed to satellite imagery that showed the site had been used for testing solid-fueled medium-range missiles and could have been used for developing longer-range missiles.

Mr. Trump holds up a document that he signed with Mr. Kim at the Capella Hotel in Singapore on Tuesday. PHOTO:SAUL LOEB/AFP/GETTY IMAGES

The meeting of the two leaders began on Tuesday at the Capella hotel on the Singaporean resort island of Sentosa at 9 a.m. local time. Mr. Trump and Mr. Kim sat down for a 38-minute one-on-one talk—the first between a sitting U.S. president and a leader of North Korea—with only interpreters present. From there, the two men were joined by their senior aides for two more hours of meetings before lunch. The two leaders then took a brief stroll without their aides before signing the document and shaking hands for the cameras.

Following the meeting, which Mr. Trump said had led to a personal bond, both sides pledged to work toward the denuclearization of the Korean Peninsula and to begin high-level negotiations at the earliest possible date.

Secretary of State Mike Pompeo and national security adviser John Bolton will meet North Korean officials next week “to go over the details” of Tuesday’s agreement, Mr. Trump said.

But the document, which Mr. Trump described as “very comprehensive,” provided almost no particulars on how to come to a speedy denuclearization that was complete, verifiable and irreversible—oft-stated U.S. goals.

In many ways, the language echoed an agreement signed between North and South Korea in April in its broad aims. It didn’t codify Pyongyang’s unilateral moratorium on nuclear and missile tests, or contain any reference to sanctions relief. It made a general pledge to a security guarantee for North Korea but didn’t mention the status of U.S. military forces in South Korea.

Trump, Kim Exchange Praise at Singapore Summit

Not long ago, the U.S. and North Korean leaders were threatening each other with annihilation. But at the Singapore summit, it was all smiles and mutual appreciation between Donald Trump and Kim Jong Un. Photo: Getty

Olivia Enos, policy analyst in the Asian Studies Center at the Heritage Foundation, said that the document was “incredibly vague,” and didn’t attempt to bridge the gap between the U.S. and North Korean conceptions of denuclearization.

“This seems like just another feel-good statement similar to the one signed at the inter-Korean dialogue with little to no meat on the bones of where we go from here,” Ms. Enos said.

Other experts said that the outcome at least kept the diplomatic process moving forward.

“It is not as much as many people hoped but meets the minimum standard for a useful step forward,” said Joel Wit, a former State Department official and a senior fellow at the Stimson Center.

Sung Kim, the former top U.S. envoy on North Korea’s nuclear program who led talks with the North at the inter-Korean demilitarized zone in the run-up to Tuesday’s summit, told reporters after the declaration signing that “there’s a lot of work left.”

“The two sides are committed to working intensively,” said Mr. Kim, who is the current U.S. ambassador to the Philippines.

Still, the agreement forestalls the likelihood of any immediate hostilities and sets the stage for more high-level negotiations.

The shift to dialogue is a contrast to the situation last year, when a series of North Korean weapons tests prompted increasingly bellicose language from the U.S. president. The two leaders taunted each other and threatened nuclear attack.

Messrs. Trump and Kim would “meet again...many times,” the U.S. president said, telling reporters that he would visit Pyongyang “at a certain time” and would invite Mr. Kim to visit the White House. “We’re probably going to need another summit,” he said.

The summit outcome came as an unexpected boon for China, which has long called for the U.S. and South Korea to suspend their joint military drills in exchange for North Korea freezing its nuclear weapons and missile tests.

China applauded the summit on Tuesday and sought to press its advantage, calling for the United Nations Security Council to reconsider its sanctions on Pyongyang, even though Mr. Trump said there would be no immediate easing and the U.S. holds a veto in the body.

“Sanctions are a means, not an end,” Chinese Foreign Ministry spokesman Geng Shuang told reporters in Beijing. “We believe the Security Council should make efforts to support the current diplomatic efforts and contribute to the political settlement of the Korean Peninsula issue.”

Mr. Trump indicated sanctions would remain in place, saying the U.S. had “tremendous leverage” to sustain economic pressure on North Korea until it moved to get rid of nuclear arsenal and programs, but added: “I look forward to taking them off.”

Japanese Prime Minister Shinzo Abe, after talking by phone with Mr. Trump, called the meeting a success but said it needed to be followed by swift action.

“We will seek full implementation of U.N. Security Council resolutions based on the success of this historic meeting,” he told reporters late Tuesday.

When asked whether he was concerned by the lack of a specific timetable in the joint statement, Mr. Abe replied, “First of all, North Korea has clearly committed itself to complete denuclearization. The fact that Chairman Kim Jong Un has made a pledge to President Trump is extremely significant, in my view. And it is written in the joint statement that they will move forward swiftly. It is exactly as those words say: They must move forward swiftly.”

Mr. Abe didn’t discuss the halting of U.S.-South Korea war games.

While Tuesday’s agreement left no doubt that Washington and Pyongyang remain far apart on the subject of North Korea’s nuclear program, the two leaders appeared to engage in amicable conversation, patting each other on the back and taking a stroll around the hotel grounds.

Mr. Trump lauded Mr. Kim as “a very worthy, very smart negotiator” and at one point showed him his armored black Cadillac.

“We had a terrific day, and we learned a lot about each other and about our countries,” Mr. Trump said. “I learned he’s a very talented man. I also learned that he loves his country very much.”

Mr. Kim expressed his gratitude to the U.S. leader for making the summit possible, and said he wanted to “leave the past behind.” “The world will see a major change” as a result of their talks, he said.

For the North Korean leader, the Singapore summit was a public-relations coup, cementing his place on the world stage during his fourth trip abroad as leader. The night before his meeting with Mr. Trump, Mr. Kim went on a sightseeing tour of Singapore, posing for selfies with local officials and waving to curious onlookers.

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Photos: Trump and Kim in Singapore for U.S.-North Korea Summit

President Donald Trump and North Korea’s Kim Jong Un shook hands at the beginning of a summit in Singapore

 

 

North Korean leader Kim Jong Un and President Donald Trump sign a joint document at the end of their summit on Tuesday.

EVAN VUCCI/ASSOCIATED PRESS

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—Andrew Jeong, Niharika Mandhana and Jeremy Page contributed to this article.