The U.S. and North Korea agreed to seek complete denuclearization of the Korean peninsula following a historic summit between President Donald Trump and Kim Jong Un, yet the accord set no deadline and left the path to disarmament undefined.

Trump defended the two-page document he signed with Kim at the end of their meeting in Singapore earlier Tuesday, saying that he thinks his North Korean counterpart will live up to to it. “It’s very comprehensive,” the president said. “It’s going to happen.”

Even with Kim’s promise to eliminate his nuclear arsenal, Trump said the U.S. will maintain economic sanctions on Pyongyang until North Korea’s nuclear program is “no longer a problem.” He praised Kim for entering into negotiations with the U.S., a longtime foe.

“People thought this could never take place,” Trump told reporters. “It’s a very great day, it’s a very great moment in the history of the world.”

The signing ceremony and Trump’s news conference capped a four-hour summit in Singapore aimed at easing decades of tensions between adversaries that only last year seemed on the brink of nuclear war.

For both leaders, the summit represented a major gamble, and its outcome was being dissected around the globe for a sense of whether one of the world’s greatest security threats -- Kim’s nuclear stockpile -- can be eliminated. The talks were seen as a key first step to formally ending the Korean War, which remains unfinished after a 1953 armistice.

During the signing ceremony, Kim said the agreement “heralds a new start, leaving the past behind.” He added: “the world will witness a major change now.” He left the summit site before Trump’s news conference and didn’t address reporters on his own.

Under their agreement, Trump committed to provide unspecified “security guarantees” to Kim, as the two sides promised to continue talks. It said nothing about how the two countries would reach the goals, and “complete denuclearization” -- the key point of contention between U.S. and North Korean negotiators -- wasn’t spelled out.

The document doesn’t include the words “complete, verifiable and irreversible” -- the baseline U.S. demand for denuclearization before lifting sanctions -- and omits Kim’s previous pledges to halt missile and nuclear testing. Trump insisted that their agreement will include verification.

“It will be achieved by having a lot of people there,” he said.

Even as their accord left major questions unresolved, the two sides did succeed in striking a friendlier tone. Trump told reporters after the summit that Kim had accepted an invitation to visit the White House, and that he would be willing to make a trip to Pyongyang at the “appropriate time.”

“Our whole relationship with North Korea and the Korean Peninsula is going to a very much different situation than it has in the past,” he said.

Trump added that the U.S. military would suspend some military exercises that North Korea has regarded as a threat to its security, but offered no specifics about which war games would be affected.

Mintaro Oba, a former U.S. State Department official who worked on North Korean issues, said the declaration “was the minimum necessary to consider the summit a success -- no premature concessions, and no escalation of tensions.”

China hailed the outcome of the summit, saying the talks should spur the United Nations Security Council to revisit sanctions aimed against Pyongyang.

“Sanctions are a means not an end,” said Geng Shuang, a spokesman for the Chinese Ministry of Foreign Affairs. “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.”

Trump and Kim kicked off their summit with a handshake shortly after 9 a.m. local time Tuesday -- 9 p.m. Monday in New York -- marking the first face-to-face encounter between a sitting U.S. president and a North Korean leader.

As the meeting opened at the Capella Hotel on Singapore’s Sentosa Island, the two men entered with somber expressions that quickly gave way to smiles. Moments earlier, Trump had announced his chief economic adviser, Larry Kudlow, had been sent to the hospital after suffering a heart attack.

“It’s my honor, and we will have a terrific relationship, I have no doubt,” Trump said in brief remarks to reporters moments after their history-making handshake.

“It was not an easy journey,” Kim said earlier. “We’ve had a past that stopped us from advancing, and wrong behaviors and practices sometimes closed our eyes and ears.”

Trump was joined in the talks by Secretary of State Mike Pompeo, who played a crucial role setting up the summit, National Security Adviser John Bolton and Chief of Staff John Kelly. Kim was accompanied by North Korean Vice Chairman Kim Yong Chol, Foreign Minister Ri Yong Ho and former Foreign Minister Ri Su Yong.

Just meeting with Trump marks a diplomatic accomplishment for Kim, who has emerged from isolation in recent months and rapidly increased his outreach to other world leaders.

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By sitting down with an American president -- a longtime goal of North Korea’s government -- Kim’s regime is advancing its effort to establish its “reputation, respect, and credibility as a nuclear weapon state,” said Michael J. Green, senior vice president for Asia and Japan Chair at the Center for Strategic and International Studies.

Trump wants the complete, verifiable and irreversible dismantling of North Korea’s nuclear weapons program. Kim is seeking a security guarantee -- and possibly a peace treaty -- and the removal of the U.S.’s nuclear umbrella protecting allies South Korea and Japan.

Kim has rejected calls to unilaterally give up his weapons in return for economic aid, and instead has proposed a step-by-step denuclearization process. His public statements and state-run media indicate he wants a deal to ease sanctions, but that he won’t give up his nuclear weapons until he feels safe enough to retain power without them.

Shortly after agreeing to the meeting in March, Trump used grandiose language to describe its prospects--at one point saying that North Koreans had already agreed to give up their nuclear weapons.

In recent weeks, however, Trump significantly scaled back his public expectations for what meeting Kim would accomplish -- at one point he referred to it as a “get-to-know-you situation.” He also began saying that it would likely take several meetings to accomplish his goal, downplaying the importance of the first summit.

Yet Pompeo on Monday drew a firm line, saying the U.S. plans to keep sanctions in place until North Korea eliminates its nuclear weapons capability. Complete, verifiable, irreversible denuclearization, he told reporters, “is the only outcome that the United States will accept.”

Yet the top U.S. diplomat added Trump is ready to offer “unique” guarantees to ease the regime’s concerns about giving up a nuclear arsenal that provides a deterrent against foreign adversaries while also serving as a key point of national pride.