HANOI, Vietnam — President Donald Trump and North Korean leader Kim Jong-un abruptly cut short their two-day summit Thursday, with talks collapsing amid differing accounts of why both leaders walked away without an agreement or a clear plan on how to keep the dialogue alive.

The fundamental disagreements rested on the trade-offs between the United States providing relief from sanctions and North Korea’s steps to dismantle its nuclear weapons program.

The two leaders and their delegations left the meeting site in Vietnam’s capital without sitting for a planned lunch or participating in a scheduled signing ceremony.

The breakdown raised serious doubts about whether the two sides can keep the diplomatic outreach moving forward. A possible U.S.-North Korea chill could also have wider spillover into the groundbreaking exchanges between the North and U.S. ally South Korea.

Trump said the main impediment to a deal was Kim’s requirement that the United States lift all economic sanctions on North Korea in exchange for the closure of one nuclear facility, which still would have left Pyongyang with a large arsenal of missiles and warheads.

But Trump also raised concerns about North Korea’s concealment of parts of its nuclear industry.

Hours later, North Korea’s foreign minister, Ri Yong Ho, offered a slightly different take at a rare news conference, arguing that Kim’s regime sought only “partial” sanctions relief in return for dismantling the North’s main enrichment capabilities for fissile material.

In a separate news conference, North Korea’s vice foreign minister, Choe Son Hui, suggested that Kim had “lost the will to engage in dealmaking” as the talks unraveled. The United States, she said, was missing a “once-in-a-lifetime opportunity,” and she said no future meetings between the two sides were planned.

“We had some options, but at this time we decided not to do any of the options,” Trump said. He added, “Sometimes you have to walk, and this was just one of those times.”

White House press secretary Sarah Sanders told reporters that Trump was aware of the North Korean statements about what happened at the summit. She made no other comments.

For Trump, the surprising turn of events amounted to a significant diplomatic setback. The president flew 20 hours to Vietnam with hopes of producing demonstrable progress toward North Korea’s denuclearization, building upon his first summit with Kim, last summer in Singapore.

The breakdown sent shivers through financial markets in Asia, with South Korea’s stock market falling sharply just before the close of trading to end down 1.8 percent.

The South Korean won also slipped, and Japan’s main Nikkei 225 index ended down 0.8 percent. On Wall Street, the Dow Jones industrial average was down.

At a news conference before he left Vietnam to return to Washington, Trump said he and Kim did not commit to holding a third summit. Still, he said, they parted ways on positive terms.

“This wasn’t a walkaway like you get up and walk out,” Trump told reporters. “No, this was very friendly. We shook hands. . . . There’s a warmth that we have, and I hope that stays. I think it will. But we’re positioned to do something very special.”

Choe, North Korea’s vice foreign minister, was less optimistic.

“The impression I got observing this summit from the side was that our chairman seems to have difficulty understanding the U.S. way of reckoning,” she said. “I felt that our chairman has lost the will to engage in dealmaking, with the U.S. saying that even a partial lifting of sanctions for the civilian economy is hard.”

The United States says U.N. sanctions cannot be unwound until North Korea fully denuclearizes. But it had left open the door to some marginal relief of unilateral U.S. sanctions if North Korea took steps in the right direction.

North Korea’s foreign minister said the North had sought an end to “sanctions that hamper the civilian economy, and the livelihood of all people in particular,” citing five out of 11 sanctions packages imposed by the U.N. Security Council.

While not total sanctions relief, that would have amounted to a significant easing of the pressure on North Korea.

Trump said Kim promised he would not conduct missile launches or test nuclear weapons. In return for sanctions relief, he said, Kim was willing to close the Yongbyon Nuclear Research Center, the site of North Korea’s main nuclear reactor and its only source of plutonium to make bombs. But Trump said Kim did not offer to close other, covert facilities to enrich uranium.

“I think they were surprised we knew,” he said. “We know the country very well, believe it or not. We know every inch of that country, and we have to get what we have to get.”

Ri, North Korea’s foreign minister, later confirmed that the North would be willing to “permanently dismantle all the nuclear material production facilities” at the main Yongbyon nuclear site and allow U.S. nuclear experts to observe.

He did not mention uranium enrichment facilities at other sites, leaving doubts about the North’s sincerity in the talks.

“It is difficult to say whether there might be a better agreement than the one based on our proposal at current stage,” Ri said. “Our principal stance will remain invariable, and our proposal will never be changed, even though U.S. proposes negotiation again in the future.”

Trump zeroed in on sanctions as the key sticking point.

“It was about the sanctions,” he said. “Basically, they wanted the sanctions lifted in their entirety, and we couldn’t do that. They were willing to denuke a large portion of the areas that we wanted, but we couldn’t give up all of the sanctions for that.”