Mr Pompeo told South Korean President Moon Jae-in the United States and North Korea agreed to continue consultations to determine a date and venue for the second Trump-Kim summit, according to the South's presidential Blue House.
Pompeo and Kim also agreed to form a working group "at an early date" to discuss the denuclearization process and the second summit, which Kim proposed to U.S. President Donald Trump in a letter last month, according to Moon's press secretary Yoon Young-chan.
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 worldwide inspectors and closing its main Yongbyon nuclear complex should the US take "corresponding measures".
As the pair sat for lunch, Kim said, "It's a very nice day that promises a good future for both countries".
Pompeo said the USA wants to coordinate closely with Japan during denuclearization talks with North Korea.
In Tokyo, Pompeo told Abe that the US wanted to work closely on nuclear talks and that he would raise with the North Koreans the issue of Japanese abductees held for decades by the regime.
Last month the North's foreign minister told the United Nations there was "no way" his country would disarm first as long as tough USA sanctions remain against his country.
A US official who was part of Pompeo's delegation said the trip was "better than the last time" but added: "It's going to be a long haul". He said they would develop options, if not finalize, the location and timing of a second Trump-Kim summit.
Pompeo said he and Kim discussed denuclearization steps to be taken by the North and the issue of USA government monitoring of those actions, which Washington sees as vital, as well as the measures the United States would conduct in return, Moon's office said.
On his way to Asia, Pompeo stuck to his guns, indicating that the spirit of the June agreement between Trump and Kim at Singapore in June 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". "And we had a very successful morning, so thank you and I am looking forward to our time here at lunch as well", Pompeo said. Pompeo arrived in Tokyo for talks with Japanese officials ahead of his trip to North Korea.
"President Trump wants the second meeting, and I think he can nearly spin anything coming out of North Korea to make the second summit happen anyway", said Terry.
Secretary of State Mike Pompeo briefs reporters at the State Department in Washington. Tension between the two governments also surfaced at last month's U.N. Security Council meeting when President Trump accused the Chinese government of trying to interfere in the U.S.'s upcoming midterm elections.
North Korea denounced Pompeo on his previous trip to Pyongyang in July for making "gangster-like demands".
This photo taken from U.S. Secretary of State Mike Pompeo's tweet on October 7, 2018, shows him meeting with North Korean leader Kim Jong-un (L) in Pyongyang.
He 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.
In an interview with the Washington Post, she said the North could agree to dismantle Yongbyon, its signature nuclear site.
But several experts told ABC News that North Korea hadn't done enough yet to earn an end-of-war declaration, let alone a second Trump-Kim summit.
Nauert also could not name who Pompeo would be meeting with in Beijing - just that "there's the expectation that he meets with someone who's his appropriate counterpart".