The United States and North Korea are technically still at war - a stop-gap armistice ended the brutal three-year Korean war in 1953 and around 30,000 American troops remain in neighboring South Korea, which the U.S. supported in the conflict.
"We had good conversations about the histories of our two nations, the challenges that we have had between us", Pompeo told reporters at a news conference with South Korea's visiting foreign minister Kang Kyung-wha Friday.
Pompeo's surprise visit to North Korea appeared to be fruitful, as he returned with three Americans who had been held in North Korean labor camps.
Politics in the Korean Peninsula is witnessing rapid changes, with both North Korea and South Korea coming together after decades of mutual isolation and division.
US analysts highlighted Singapore's political neutrality, geological proximity and cultural diversity. Seeing what happened to non-nuclear power Iraq, Iran and North Korea raced to build their own bombs.
Mr Kang says there must be "airtight" coordination between South Korea and the USA ahead of President Donald Trump's upcoming meeting with Mr Kim.
"As we have achieved in our maximum pressure campaign of getting people to kick out North Korean diplomats, North Koreans all around the world, that has put pressure on North Korea", she said. A meeting between the two political leaders has been in the works since Trump accepted Kim's invitation to meet in March, CNN reported. "It looks very much like the trip to Dalian was a dry run", said Andray Abrahamian, a research fellow at Pacific Forum CSIS and formerly with Choson Exchange, a Singapore-based group that trains North Koreans in business skills. "We were each representing our two countries, trying our best to make sure that we were communicating clearly, that we had a shared understanding about what our mutual objectives were".
Trump deliberately violated that deal on Tuesday in the most comprehensive manner possible, restoring all United States sanctions on Iran and threatening European and other foreign companies with crippling punitive measures if they continue to do business in Iran.
If, on the other hand, Kim offers Trump something that can be sold as a win, the president will be tempted to grab it. South Korea is an extremely wealthy nation, while North Korea is disastrously poor.
Pompeo once floated the stricter idea of "permanent" dismantlement to ensure North Korea had no capability to renew its weapons program, but the language was toned down to "complete" after his return.
This, Mr. Kang said, would prepare for the June 12 summit. He said on both shows that the objective was to prevent North Korea from having the capability to strike the United States with a nuclear weapon. But this talking point, however, ignores an equally plausible explanation: That having achieved his strategic weapons program goals, Kim is trying his hand at playing America's narcissist-in-chief.