HK GOT INT,L STRATEGIC CONSULTING LIMITED

HANOI, Vietnam — Over the past quarter-century, three American presidents have tried cajoling, threatening and sabotaging North Korea in its efforts to build a nuclear arsenal. Eventually each turned to negotiations, convinced that an isolated, broken country would surely choose economic benefits for its starving populace over the bomb.

President Trump was the fourth to test that proposition, but with a twist: Engaging in the sort of direct talks that his predecessors shunned, the president traveled 8,000 miles for his second summit meeting in less than a year with Kim Jong-un, the North Korean leader, betting that his self-described skills as a master negotiator would make all the difference.

As it turned out, they didn’t. The meeting in Vietnam ended in shambles on Thursday when Mr. Kim insisted on a full lifting of sanctions, according to Mr. Trump, and would not agree to dismantle enough of his nuclear program to satisfy American demands. The North Koreans later contradicted Mr. Trump, saying they had demanded only a partial lifting of sanctions, but they confirmed that they had offered to dismantle their main nuclear site, at Yongbyon.

The split underscored the risk of leader-to-leader diplomacy: When it fails, there are few places to go, no higher-up to step in and cut a compromise that saves the deal.

In this case, the price may be high — especially if Mr. Kim responds to the failure by further accelerating his production of nuclear fuel and a frustrated Mr. Trump swings from his expressions of “love” for the North Korean dictator and back to the “fire and fury” language of early in his presidency.

“No deal is better than a bad deal, and the president was right to walk,” said Richard Haass, the president of the Council on Foreign Relations.

“But this should not have happened,” he said. “A busted summit is the risk you run when too much faith is placed in personal relations with a leader like Kim, when the summit is inadequately prepared, and when the president had signaled he was confident of success.”

The outcome on Thursday took everyone by surprise. Mr. Trump was so convinced a deal was in the offing that the White House had announced that a “signing ceremony” would be held immediately after a warm lunch between the two leaders. But no one ever sat down at the elegantly set table in the century-old Metropole Hotel, and there was no signing ceremony because there was no communiqué to sign.

For his part, Mr. Kim seemed to think he had Mr. Trump exactly where he wanted him: desperate for a deal, and in need of a headline-making victory after the devastating testimony on Monday of Michael D. Cohen, Mr. Trump’s former lawyer and fixer.

If so, Mr. Kim clearly miscalculated.

“Trump could have had a small deal,” Joseph Yun, the former State Department special envoy for North Korea, said after the collapse on Thursday. “Close a few sites, and lift a few sanctions. But because of Cohen, the president needed a big deal” — one that traded sanctions relief for the mass dismantlement of nuclear infrastructure that it took the North Koreans the better part of 40 years to construct.

In the short run, the damage from the failed meeting is likely to be considerable, and not just to Mr. Trump’s dreams of a Nobel Peace Prize, which he asked Japan’s prime minister, Shinzo Abe, to nominate him for.

The risk now is that having placed their personal imprimatur on the negotiations, Mr. Trump and Mr. Kim will be tempted to raise the pressure on each other.

That could herald a new era of nuclear tensions, at a moment when a major arms control deal with Russia has been declared dead, when India and Pakistan are once again reminding the world of the risks when two nuclear-armed states start skirmishing, and when Iran is weighing restarting its nuclear fuel production.

History suggests that the North Koreans may try to pressure Mr. Trump by escalating. And they have the opportunity: Mr. Trump not only left Hanoi early, but he also left without any agreement for a “freeze” on continued North Korean production of nuclear material. That means that the world’s fastest-growing nuclear arsenal will continue to increase in size as negotiations drag on.

In retrospect, there were warning signs that things were going south.

When Secretary of State Mike Pompeo went to Pyongyang to turn a vaguely worded agreement to pursue denuclearization struck at the June meeting in Singapore into reality, Mr. Kim declined to see him. When he returned, he got an audience — but no inventory of North Korea’s nuclear weapons, its production facilities and its missiles. Without that, there was no way for the two sides to agree on a timetable for dismantlement.

For months, the North declined to deal with the State Department’s special envoy, Stephen Biegun. And when the North Koreans did, they explored many options, but made clear sanctions relief had to come first.

Mr. Trump made his own situation worse. He kept repeating that there was “plenty of time” to reach an agreement, taking all the urgency out of the issue.

When The New York Times and The Wall Street Journal reported on satellite evidence and expert analysis suggesting that the North was still producing nuclear material and expanding missile bases, Mr. Trump said on Twitter that there was no news in those reports. He blamed the media for making a big deal of it — rather than having used the moment to remind the North Koreans that its activities were being intensely monitored, and not just by spy satellites.

And on Wednesday night, when the two men met again at the Metropole, it was clear from the body language that something had changed since their first warm embrace in Singapore eight months ago.

Mr. Trump, who said over the weekend that he would be happy just to have a continued ban on missile and nuclear testing, realized that if he acceded to Mr. Kim’s demand for an end to sanctions, he would lose whatever leverage the United States possessed.

“I’d much rather do it right than do it fast,” the president told reporters before leaving Hanoi early.

One of the most telling obstacles in the negotiations was over a facility called Kangson, which the North Koreans have never publicly acknowledged. Detected by American intelligence agencies nearly a decade ago, the site, in a suburb of the capital, Pyongyang, is believed to be a secret nuclear enrichment plant.

Mr. Trump’s team of negotiators believed that the North’s willingness to let inspectors into the plant, and ultimately shutter it, would be a good test of Mr. Kim’s commitment to denuclearization.

For years, the American knowledge of the site was highly classified, and never discussed. But when asked by a reporter at a news conference on Thursday whether Mr. Kim had been unwilling to deal with its fate, Mr. Trump acknowledged that was one of the problems, along with other facilities “they were surprised we knew.”

“I think it is very positive that the Trump administration sought constraints at previously undisclosed facilities outside Yongbyon,” Robert J. Einhorn, one of the senior arms control experts who worked for the administrations of Bill Clinton and Barack Obama. Preventing North Korea from producing new fuel, he said, “would be a much better indication of North Korea’s willingness to go down the denuclearization track than simply closing Yongbyon, which would not halt their production of all bomb-making nuclear material.”

By Mr. Trump’s account, Mr. Kim would not take up such issues until the world lifts the economic pressure on North Korea. “He wants the sanctions off,” he said.

Now the question is whether Mr. Trump will continue his form of personal-relationship diplomacy or decide that the risks are too great, and that he should return to the step-by-step approach most of his predecessors used.

“Look, there has to be a reason for the conversations,” Mr. Pompeo told reporters late Thursday, on his way to the Philippines. “There has to be a theory of the case of how to move forward. I’m confident there is one.”

He just didn’t say what it was.