In South Korea, Pompeo appeared alongside President Moon Jae-in, who said the world wanted to know the results of the Pyongyang meeting, "so if the secretary can disclose the results, please tell us".
In his first communication after meeting Kim, Pompeo tweeted: "Had a good trip to #Pyongyang to meet with Chairman Kim". President Trump sends his regards. But as of Sunday night, there were few details and no apparent outcome, nor had any early-morning White House tweets on the meeting appeared - indicating that it may not be before Pompeo returns to the United States that more details emerge.
South Korea's government also said the North is not prepared to produce a list of nuclear sites at this stage in the negotiations.
As Pompeo and Kim seated for their lunch meeting, Kim, without specifically mentioning any topics up for discussion, said it was a "very nice day that promises a good future for both countries".
But Pompeo is downplaying expectations for the trip, even with the pressure on from allies and adversaries in the region who want to begin easing sanctions on North Korea and from critics back home who point to the regime's lack of verifiable, irreversible steps to dismantle its nuclear arsenal. It has not taken any steps to halt nuclear weapons or missile development.
Before traveling to Pyongyang, Pompeo met in Tokyo on Saturday with Japanese Prime Minister Shinzo Abe and Foreign Minister Taro Kono.
South Korean President Moon Jae-in (R) shakes hands with United States Secretary of State Mike Pompeo during their meeting at the presidential office in Seoul on October 7, 2018.
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At the same time, the debate over whether to treat North Korea as a de facto nuclear power could influence whether fragile diplomacy continues or Northeast Asia returns to the threats of nuclear strikes that had many fearing war just past year. He said they would develop options, if not finalize, the location and timing of a second Trump-Kim summit.
At the outset of his talks with Moon, Pompeo said South Korea is playing an important role in the denuclearization process.
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.
"Each side has to develop sufficient trust so they can take the actions necessary to get to the end", Pompeo said.
The top United States diplomat offered no details, and, upon landing in South Korea, he briefed White House national security adviser John Bolton and Trump chief of staff John Kelly on his trip, officials said.
Trump, however, has continued to praise his relationship with Kim.
The North has committed to taking additional denuclearization steps, such as shutting down its long-range missile engine test site and launching pad in Dongchang-ri on the west coast in the presence of global inspectors and closing its main Yongbyon nuclear complex should the USA take "corresponding measures".
South Korean foreign minister Kang Kyung-wha has given a hint of what a grand bargain between the two countries could look like.
On Monday, Pompeo is expected to land in Beijing - the last stop on his whirlwind diplomatic tour. "Maybe we will get further than that", said the top United States diplomat.