Washington's focus is on disarming Kim's regime, which has recently tested what appear to be missiles capable of carrying his nuclear threat to U.S. cities.
Kim has also twice visited China after failing to pay his respects to President Xi Jinping in the six years since he inherited power from his father.
We are closing out a dramatic week for diplomacy in Asia.
Their releases draw a line under an issue that had weighed on plans for the historic summit between Kim and Trump that will focus on North Korea's nuclear weapons.
Pompeo made the remarks at a joint news conference with South Korean Foreign Minister Kang Kyung-wha in Washington on Friday.
I wish we had a president with common sense, because then I could warn him about North Korean leader Kim Jong Un. It was embarrassing to see how Trump was with French President Emmanuel Macron.
"It is regrettable that North Korea did not invite nuclear experts to the destruction of the test site", it said in an editorial.
"I feel we've a shared imaginative and prescient for what we hope, when this course of is accomplished, the Korean peninsula appears like, I feel we've a very good understanding and I feel there's full settlement of what the last word aims are", Pompeo stated, including that, "we started to work via the modalities of how we obtain that".
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"We wish these Americans and their families the best, as they reconnect after a very hard time apart", Pompeo said.
But both Kang and Pompeo insisted that they agreed on the need for the "total, complete, permanent and verifiable" denuclearization of the divided peninsula.
Singapore also confirmed it would host the meeting, but did not give further details.
When Trump and Kim do sit down, the two relatively untested leaders will be presented with a puzzle that has stymied seasoned diplomats for decades.
Amid concerns that North Korea will demand the US withdraw its troops from neighbouring South Korea, Ms Kang emphasised that the US military presence there must be "a matter for the US-ROK alliance first and foremost", using an acronym for South Korea's official name, the Republic of Korea. Multiple rounds of non-proliferation talks have taken place, and a deal was even signed in 1994. Given North Korea's extensive and hidden nuclear program, complete verification may be impossible to achieve.
And, more than two decades and multiple provocative weapons tests after the last accord, the threat from Pyongyang has only grown.
Journalists asked Pompeo what such a denuclearization would look like and if it meant carrying out inspections in North Korean nuclear plants.
One, people wonder if North Korea's definition of denuclearization is the same as the United States'.