The top USA diplomat made the remark during his meeting with South Korean President Moon Jae-in in Seoul after visiting Pyongyang earlier in the day, according to the presidential Blue House of South Korea.
Moon expressed hope that Pompeo's trip and the proposed second meeting between Kim and Trump will make "irreversible, decisive progress in terms of denuclearization as well as the peace process".
Trump has appeared keen on a second summit with Kim, even though recent North Korean statements have suggested the two sides are far from narrowing their differences.
Pompeo originally planned to visit the North Korean capital in late August, but that trip was cancelled by Trump at the last minute due to a lack of progress in U.S.
Pompeo said he had had a "great visit" and a "very successful morning", adding that Trump sent his regards. However, details of Sunday's discussions have not been made public yet.
However, relations seemed to get a reboot following last month's inter-Korean summit and subsequent meetings between Moon and Trump, as well as between North Korean Foreign Minister Ri Yong Ho and Pompeo on the sidelines on the UN General Assembly in NY last month.
Their meeting took after Pompeo returned from his trip to Pyongyang to meet with North Korean leader Kim Jong-un earlier in the day.
In June, Trump met Kim in Singapore in the first-ever summit between the countries.
U.S. Secretary of State Mike Pompeo, left, shakes hands with Japanese Prime Minister Shinzo Abe at Abe's office in Tokyo, Oct. 6, 2018. "They believe that without nuclear weapons, they are as good as dead".
Japan, which has seen North Korean missiles fly over its territory and been threatened with annihilation, has historically taken a hard line on Pyongyang and stressed the need to maintain pressure on the regime.
US Secretary of State arrived in South Korea on Sunday after visiting North Korea. North Korea has been playing hard ball since then, accusing the United States of making "unilateral and gangster-like" demands on denuclearization and insisting that sanctions be lifted before any progress in nuclear talks occurs.
"Each side has to develop sufficient trust so they can take the actions necessary to get to the end", Pompeo said.
Washington and Pyongyang have sparred over the exact terms of their vaguely-worded agreement in Singapore, with the U.S. pushing to maintain sanctions and pressure against the North until its "final, fully verified denuclearisation".
South Korean Minister of Foreign Affairs Kang Kyung-wha has given a hint of what a grand bargain between the two countries could look like.
Pompeo plans to visit Beijing on Monday as he concludes his four-nation visit to the region that also included Japan.
"This is a busy time diplomatically", said Al Jazeera's McBride.
The top U.S. 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.
But the inter-Korean agreement again failed to stipulate any plans called for by the United States, such as to declare a list of its nuclear weapons, facilities and materials, or a concrete timeline for denuclearization.
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