Mr. Trump and his aides are expected to seek a quick timetable for the North to eliminate its nuclear weapons, mindful that it has failed to deliver on its promises in the past, including a pledge not to develop such weapons. And Friday’s agreement between Mr. Moon and Mr. Kim was notably short on specifics like timing.
“South and North Korea agreed to actively seek the support and cooperation of the international community for the denuclearization of the Korean Peninsula,” their statement said.
Fifteen minutes later, he declared in an all-caps tweet, “KOREAN WAR TO END!” and said that all Americans should be “very proud” of what was taking place on the Korean Peninsula.
In another tweet, he thanked President Xi Jinping of China for his “great help” in the process.
China’s state news media played the summit meeting prominently, even though China had been left on the sidelines with little influence over Friday’s proceedings.
The Chinese Foreign Ministry praised the courage of the two leaders, and said it welcomed “the new journey” for peace on the Korean Peninsula. Mr. Xi, who hosted Mr. Kim in Beijing last month, was preoccupied with his own summit meeting in China with India’s leader, Narendra Modi.
The tone of the Moon-Kim session — broadcast live nationally on South Korean television — was convivial and at times jocular, with Mr. Kim showing surprising honesty about the differences in conditions between the two nations.
Yoon Young-chan, Mr. Moon’s spokesman, said Mr. Kim acknowledged the poor road conditions in his country, a startling admission for a member of his ruling family, which is considered godlike and faultless among North Koreans. Mr. Kim also revealed that the North Koreans who visited the South during the Winter Olympics in February all admired the bullet train there.
After Mr. Moon spoke of wanting to visit North Korea, Mr. Kim said, “It will be very embarrassing,” alluding to roads there.
Mr. Kim also repeated a lighthearted line he had used in his meeting with South Korean envoys in Pyongyang, the North Korean capital, last month, apologizing to Mr. Moon for disturbing his sleep with missile tests and forcing him to attend meetings of his National Security Council.
“I heard you had your early-morning sleep disturbed many times because you had to attend the N.S.C. meetings because of us,” Mr. Kim said. “Getting up early in the morning must have become a habit for you. I will make sure that your morning sleep won’t be disturbed.”
Mr. Moon joked back: “Now I can sleep in peace.”
The move to end the Korean War formally would face obstacles, including China’s likely demand for the withdrawal of American troops from South Korea as part of a peace treaty. An armistice brought about a cease-fire to the Korean War in 1953, but the conflict never ended because the parties could not agree to a formal peace treaty.
The two leaders agreed on Friday that Mr. Moon would visit Pyongyang in the fall. Their statement also said that within a year, they would push for a trilateral conference with the United States, or a four-party forum that also included China, with the aim of “declaring an end to the Korean War” and intentions to “replace the armistice with a peace treaty.”
Mr. Kim and Mr. Moon also vowed to improve inter-Korean relations by opening a liaison office in the North Korean border town of Kaesong and arranging a reunion later this year of families separated by the war.
Mr. Moon also offered some capitalistic carrots during the talks, reminding Mr. Kim that South Korea had in years past promised huge investments to help improve the North’s road and train systems. Those agreements eventually collapsed as the North persisted in developing nuclear weapons.
Mr. Moon, who says he likes to see South Korea “in the driver’s seat” in pushing the peace effort forward, is trying to broker a successful summit meeting between Mr. Kim and Mr. Trump, which is expected in late May or early June.
Mr. Kim rattled the region last year by testing long-range missiles and trading threats of nuclear war with Mr. Trump. But then Mr. Kim shifted gears, saying he was willing to give up his nuclear weapons for the right incentives and proposing the meeting with Mr. Trump.
Last weekend, Mr. Kim announced an end to all nuclear and long-range-missile tests, saying that his country had mastered how to mount nuclear warheads on missiles and no longer needed to conduct tests. Mr. Kim said North Korea had adopted a “new strategic line” focusing on economic development.
Skeptics say Mr. Kim is trying to improve ties with South Korea to steer it from the United States and escape sanctions that are increasingly hurting the North’s economy. Indeed, many conservatives in the South fear that the North’s goal remains to be accepted as a nuclear power in return for freezing its nuclear and intercontinental ballistic missile programs.
Some analysts said that Friday’s inter-Korean statement, including Mr. Kim’s formal commitment to denuclearization, appears to lay the foundation for a summit meeting between him and Mr. Trump. But they urged caution.
The declaration “is breathtaking in its scope and ambition,” David Albright, president of the Washington-based Institute for Science and International Security, said by email. “But how to achieve all the goals laid out in the document, given the current situation?”
He said that unless “a firm foundation” for North Korea’s verifiable nuclear disarmament were laid out, most of the other commitments in the declaration were “merely wishes.”
Analysts have warned that once negotiations begin with the United States, North Korea could push them into a stalemate by trying to drag Washington into nuclear arms reduction talks.
To prevent that, South Korea and the United States are trying to persuade North Korea to agree to a specific timeline for complete denuclearization: as soon as possible and no later than the end of Mr. Trump’s current term, in early 2021, according to South Korean officials and analysts.
During their morning talks, Mr. Kim pushed for more summit meetings with Mr. Moon, saying he would like to visit the presidential Blue House in Seoul. He said North Korea would cooperate to make a “better world.”
But he also voiced caution, suggesting South Korea and the United States deserved blame for scuttling previous deals.
“As the expectations are high, so is the skepticism,” he said. “In the past, we had reached big agreements, but they were not implemented for more than 10 years. There are people who are skeptical that the results of today’s meeting will be properly implemented.”