Vice Foreign Minister Choe Son Hui emphasized at a news conference in Pyongyang that the two leaders maintain a good relationship after the summit ended without a deal. And U.S. Secretary of State Mike Pompeo played down tensions, responding in Washington that he expected that the two sides would continue “very professional conversations.”

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Yet behind the scenes, Trump aides have struggled to articulate a path to bridge the wide gaps between Washington’s demands that the North fully dismantle its nuclear weapons program and Pyongyang’s insistence that the United States ease punishing economic sanctions in exchange for incremental steps.

In a private briefing in Washington this week, one White House official told foreign-policy analysts that Trump’s talks with Kim last month convinced the president that the regime is unwilling to surrender its nuclear program, said Sue Mi Terry, a Korea expert at the Center for Strategic and International Studies who attended the briefing.

“What he was saying is that everybody knew North Korea would not give up its nukes, but Trump was not sure,” she said. “And, most significantly, that Trump finally gets that fact, and it’s not easily solvable.”

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That realization throws into question Trump’s strategy of abandoning the precedent of past U.S. administrations that rejected presidential-level talks, choosing instead to engage in direct negotiations with Kim — without a clear road map for how a denuclearization process would work. Since their first summit in Singapore last June, there had been little progress among working-level negotiators, and the Hanoi summit failed to punch through the fundamental disagreements.

Some foreign-policy experts suggested that the sharp language from Choe was typical of Pyongyang’s negotiating tactics and were aimed at winning leverage rather than scuttling talks. The vice minister accused Pompeo and national security adviser John Bolton, both of whom accompanied Trump to Hanoi, of creating an atmosphere of “hostility and mistrust,” but she did not directly criticize Trump.

“The chemistry is mysteriously wonderful,” Choe said of Kim and Trump’s relationship.

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Bolton called Choe’s characterization of the Hanoi talks “inaccurate,” while Pompeo noted that he had been the focus of North Korean umbrage after a trip he made to Pyongyang last July.

A White House spokesman declined to comment.

Kim’s efforts to woo Trump, which have included sending him flattering personal letters, could have diminishing returns, given the failure in Hanoi. U.S. officials said the president’s willingness to walk away without a deal would help empower the administration’s negotiating team, led by special envoy Stephen Biegun, who has been frustrated in working-level meetings with his counterparts in Pyongyang.

During an appearance this week at the Carnegie Endowment for International Peace, Biegun emphasized that the administration would not lift sanctions until the North completely dismantled its nuclear program and ballistic missiles.

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Asked whether Kim might resume missile testing after a 16-month moratorium, Biegun replied: “The short answer is: We don’t know. What Kim Jong Un will decide to do may very much be his decision and his decision alone.”

Trump said this month that he would be “very disappointed” if the North followed through with a test, after satellite images showed construction underway to rebuild the Sohae rocket launch facility.

At a news conference in Hanoi, Trump said several times that Kim had promised him that he would maintain the testing freeze, which the president has cited as evidence that his negotiations have made progress even though North Korea went through longer moratoriums during past U.S. administrations. As recently as February, Trump suggested that he should be awarded the Nobel Peace Prize for his efforts with North Korea and complained that the news media have not given him enough credit.

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Trump “indicated that nuclear and missile testing really is a red line. He basically said that as long as they’re not testing, he’s happy, even though behind the scenes they continue to perfect their arsenal,” said Bruce Klingner, a former U.S. intelligence official who is now a Northeast Asia analyst at the conservative Heritage Foundation.

A test “certainly closes the book on diplomacy,” Klingner added. “I think the U.S. is trying to figure out where to go. The president is now less optimistic.”

After returning from Hanoi, Trump aides sought to shore up political support, briefing lawmakers on Capitol Hill and other stakeholders and making the case that the president had showed his negotiating fortitude by holding a hard line on sanctions and being willing to walk away without a deal on his top foreign-policy initiative.

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At one briefing, according to one person in the room who spoke on the condition of anonymity to discuss the private meeting, Biegun told congressional staffers that the North Koreans were not creative in their thinking and did not appear to have a “plan B” after the United States rejected a proposal to lift most sanctions in return for the closure of some of the Yongbyon nuclear site, the country’s main production site for fissile materials.

Yet Biegun also took pains to emphasize that he had not assumed his job until last fall, well after the first Trump-Kim summit, which some lawmakers and staffers interpreted as a signal that he felt he had inherited a difficult portfolio and did not want to be blamed for the breakdown in talks.

“I honestly don’t know what they do next. I think this has devolved even from the week we sat down” for the briefing, said the person who was at Beigun’s briefing. “The more that Pyongyang is demonstrating its resolve and the more we make hard-line statements that demonstrate our resolve, the harder it is to figure out how to get back to the negotiating table.”

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After the administration’s outreach efforts, a bipartisan coalition of lawmakers offered public praise last week for Trump’s approach, affirming his decision to reject Pyongyang’s offer in Hanoi. But former U.S. officials who have negotiated with the North Koreans said the tougher rhetoric since the summit was evidence that the engagement process was showing signs of collapsing.