North Korean leader Kim Jong Un and U.S. Secretary of State Mike Pompeo agreed to arrange a second summit between the two countries as soon as possible, South Korea’s presidential office said on Sunday.

South Korea’s President Moon Jae-in met Pompeo after the top U.S. diplomat’s trip to Pyongyang earlier in the day, which included a meeting with Kim.

Pompeo told Moon that he and Kim discussed denuclearization steps to be taken by North Korea and the issue of inspection on those actions, which Washington has been calling for, as well as the measures the United States would take, Moon’s press secretary Yoon Young-chan said in a statement.

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Pompeo and Kim also agreed to form a working group to discuss the denuclearization process and the second summit between Kim and U.S. President Donald Trump, Yoon said.

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Arriving in Seoul after spending several hours in Pyongyang on his fourth visit to North Korea, Pompeo tweeted that he had a “good trip” and that he and Kim “continue to make progress on agreements made at Singapore summit,” referring to the historic June meeting between Trump and Kim that resulted in a vague agreement for the North to denuclearize.

He offered no details and upon landing in South Korea briefed White House national security adviser John Bolton and chief of staff John Kelly on his trip, officials said. Pompeo, on the third stop of a four-leg trip that began in Japan and will end in China on Monday, then met South Korea’s President Moon Jae-in, who has met twice with Kim and asked Pompeo to make public as much information as he could about the trip.

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Pompeo declined the opportunity, saying: “I will certainly tell you in private about our conversation, but we had a good, productive conversation. As President Trump said, there are many steps along the way and we took one of them today. It was another step forward. So this is, I think, a good outcome for all of us.”

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In Pyongyang, Pompeo and Kim met for about 3 1/2 hours, first in a business session and then in a 90-minute luncheon that the North Korean leader hosted at a state guesthouse, according to the pool report of the lone U.S. journalist allowed to accompany the secretary on his trip.

“It’s a very nice day that promises a good future for both countries,” Kim told Pompeo through an interpreter as they sat down for the meal.

“Yeah, so we had a great, great visit this morning,” Pompeo replied. “Thank you for hosting, President Trump sends his regards. And we had a very successful morning so thank you and I am looking forward to our time here at lunch as well.”

On the North Korean side, Kim was joined at the lunch by his sister Kim Yo Jong and his former intelligence chief Kim Yong Chol, who has been Pompeo’s chief interlocutor. Aside from Pompeo, the U.S. side included Stephen Biegun, the new U.S. special envoy for North Korea, and Andrew Kim, who heads a Korea working group at the CIA that Pompeo set up while he was running the agency.

The two men had exchanged pleasantries and appeared chummy while they walked into the banquet room. “It’s good to see you again,” Pompeo said as they shook hands and Pompeo placed his hand on Kim’s shoulder and they both smiled. “So is everything OK?” Kim asked Pompeo. “Everything is great,” he replied. “Everything is great. I am very much looking forward to our time together too.”

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Other members of the two delegations ate their five-course meal – which included delicacies such as foie gras, conch soup, steak, grilled pine mushrooms and chocolate cake, sweet red wine and soju – in a separate room.

Pompeo had planned to meet with Kim on Sunday’s trip – his third to Pyongyang as secretary of state – but North Korean officials said Kim’s participation in the luncheon had not been expected. Pompeo had not met with Kim on his last visit and Trump had abruptly cancelled his top diplomat’s plans to travel to North Korea last month, citing a lack of progress in the negotiations

One U.S. official who accompanied Pompeo said Sunday’s meeting was “better than the last time,” but added that “it’s going to be a long haul.” The official was not authorized to discuss the negotiations publicly and spoke on condition of anonymity.

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Pompeo had flown to Pyongyang from Tokyo after talks there with Japan’s prime minister during which he pledged the Trump administration would co-ordinate and unify its strategy for denuclearization with allies. Japan has been wary of the initiative, but South Korea has embraced it.

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Pompeo has repeatedly refused to discuss details of negotiations, including a U.S. position on North Korea’s demand for a declared end to the Korean War and a proposal from Seoul for such a declaration to be accompanied by a shutdown of the North’s main known nuclear facility.

The U.S. and Japan have pushed for the North to compile and turn over a detailed list of its nuclear sites to be dismantled as a next step in the process; the North has rejected that.

Since the denuclearization effort got underway with a secret visit to the North by then-CIA chief Pompeo in April, there has been only limited progress, even since the June 12 Trump-Kim summit in Singapore that many had hoped would jump-start the effort.

North Korea so far has suspended nuclear and missile tests, freed three American prisoners and dismantled parts of a missile engine facility and tunnel entrances at a nuclear test site. It has not taken any steps to halt nuclear weapons or missile development.

The North also has accused Washington of making “unilateral and gangster-like” demands on denuclearization and insisted that sanctions should be lifted before any progress in nuclear talks. U.S. officials have thus far said sanctions will remain in place until the North’s denuclearization is fully verified.

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Pompeo said in Tokyo that it was important to hear from the Japanese leader “so we have a fully co-ordinated and unified view.” He also pledged that during his meeting with Kim on Sunday, he would raise the cases of Japanese citizens abducted by North Korea.

–With files from Reuters.