“It’s good to see you again,” Pompeo told Kim as the two men shook hands for the cameras before lunch. The secretary of state then put his hand on Kim’s shoulder, and the pair smiled.

“Well, I am really pleased for this opportunity. After having a nice meeting, we can enjoy a meal together,” Kim said.

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As the pair sat for lunch, Kim said, “It’s a very nice day that promises a good future for both countries.”

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Pompeo said he had a “great visit” and a “very successful morning,” adding that Trump sent his regards. Both men spoke through interpreters.

The secretary of state’s previous trip to North Korea, in July, did not go so well. He came away from it saying the two sides had made progress, only for North Korea to denounce him for making “gangster-like” demands and raising “cancerous” issues. On that occasion, he did not meet with Kim.

Pompeo then planned to return in late August, only for Trump to cancel the trip at the last minute as it became apparent that the two sides remained far apart on their approach to the negotiations.

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But a summit of the leaders of North and South Korea last month has helped to rekindle the peace process, as has the apparent desire of both Kim and Trump to meet again.

An official accompanying the delegation who spoke on the condition of anonymity said the trip had gone “better than the last time” but added that it is going to be a “long haul,” according to a pool report from the lone U.S. journalist who accompanied Pompeo to Pyongyang.

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Later Sunday, Pompeo flew to Seoul, where he met with South Korean President Moon Jae-in. He said in Seoul that he had had “a good, productive conversation” with Kim.

“As President Trump said, there are many steps along the way, and we took one of them today,” Pompeo said. “It was another step forward. So this is, I think, a good outcome for all of us.”

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Moon said he hoped a Trump-Kim summit would happen soon and “make irreversible, decisive progress in terms of denuclearization as well as the peace process.”

During his private meeting with Moon, Pompeo said he and Kim had agreed to arrange the second U.S.-North Korea summit “at the earliest possible date,” according to a statement issued by Moon’s chief press secretary, Yoon Young-chan.

“Secretary Pompeo said there had been discussions on denuclearization measures to be taken by North Korea and monitoring by the U.S. government, as well as on corresponding measures to be taken by the United States,” Yoon said.

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Yoon said the two sides would form “working-level negotiating teams” to discuss the specific date and location for the summit, as well as North Korea’s denuclearization process.

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During Pompeo’s meeting in Pyongyang, Kim invited inspectors to visit the Punggye-ri nuclear test site to “confirm that it has been irreversibly dismantled,” a State Department spokeswoman, Heather Nauert, said in a statement. North Korea had committed to this previously but has been resistant to allowing international inspectors to visit sites it has claimed have been dismantled.

“Allowing inspectors at Punggye-ri would be an important test of North Korea’s willingness to subject its facilities to verification,” said Adam Mount, a senior fellow at the Federation of American Scientists.

Nauert’s statement made no mention of North Korea’s commitment to dismantle the important Yongbyon nuclear facility, a potentially troubling sign for U.S. negotiators.

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At the heart of the impasse has been two fundamentally different approaches to denuclearization.

Pompeo has insisted that sanctions on North Korea should remain in place until the country completely dismantles its nuclear program.

The governments of both North and South Korea, however, say that is unrealistic. Instead, they want both sides to take a “phased” approach, in which Pyongyang is rewarded as it takes gradual steps to roll back its nuclear program.

On his way to Asia, Pompeo stuck to his guns, indicating that the spirit of the June agreement between Trump and Kim in Singapore was that “we will get to denuclearization in a fully verified, irreversible way, and then we will actually deliver on the commitments to make this brighter future for the North Korean people.”

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Pompeo met with Japanese Prime Minister Shinzo Abe in Tokyo on Saturday, and the two men “agreed that pressure must continue until the DPRK [Democratic People’s Republic of Korea] denuclearizes,” Nauert said.

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That is not how Pyongyang sees things, nor is it the approach being advocated for by Seoul.

After the summit between the leaders of the two Koreas last month, Kim said he was prepared to permanently dismantle his country’s main nuclear site at Yongbyon, but only if the United States took “corresponding steps” to build trust.

North Korea has been asking for the United States to declare the 1950-1953 Korean War formally over, as a way to end hostile relations between the two countries. The war concluded with an armistice but no peace treaty.

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In the past few days, North Korea has also renewed its demands for sanctions to be eased.

North Korean Foreign Minister Ri Yong Ho told the U.N. General Assembly late last month that “coercive” sanctions were lethal to trust-building between the two nations and that without trust, “there is no way we will unilaterally disarm ourselves first.”

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Pompeo was to visit Beijing on Monday as he concludes his four-nation visit to the region.