The U.S. would even help the North Korean economy if it takes "bold action to quickly denuclearize," the top U.S. diplomat added.
Pompeo met with South Korean Foreign Minister Kang Kyung-wha in Washington one day after bringing three American detainees home from Kim's custody and ahead of South Korean President Moon Jae-in visit the White House May 22.
After months of fiery rhetoric and increasingly strong international sanctions, Trump and Kim are set to meet in Singapore on June 12 to discuss denuclearization. But there have been questions about whether or not North Korea and the U.S. have the same understanding of what that means – and whether Kim is really willing to give up a nuclear program begun by his grandfather, a man he idolizes.
"We have a shared vision for what we hope when this process is completed the Korean Peninsula looks like," Pompeo said Friday. "We have a good understanding, and I think there is complete agreement about what the ultimate objectives are."
Pompeo added that in his meetings with North Korean officials Wednesday, including Kim, they began to work on how to achieve that.
In exchange for that U.S. demand – one that many believe North Korea isn't seriously considering – the U.S. is willing to offer economic assistance, Pompeo said, promising "a future brimming with peace and prosperity."
"If North Korea takes bold action to quickly denuclearize, the United States is prepared to work with North Korea to achieve prosperity on the par with our South Korean friends," Pompeo said.
Until then, however, the international sanctions will remain in place, Foreign Minister Kang said.
In an interview with ABC News Chief White House Correspondent Jonathan Karl, Pompeo was less clear, saying, "We’ll see how the negotiations proceed," and repeating, "We have our eyes wide open."
Kang's comments didn't clear up the discrepancy: "We've been very clear that the sanctions remain in place until and unless we see visible meaningful action taken by North Korea on the denuclearization track," she said, but it's unclear how far down that "track" North Korea must be before they get sanctions relief.
One thing that is not up for negotiations, she said, was the U.S. military presence in South Korea -- something that North Korea has long desired to end, as it seeks to reunify the Korean peninsula under its control.
"The troop presence in our country is a matter for the two allies to discuss and not to be put on the table with North Korea," Kang said Friday.
Any deal will also "require a robust verification program," Pompeo said, although it's hard to underscore how difficult that process would be. North Korea's mountainous geography and years of insularity would make ensuring North Korea had verifiably given up its entire nuclear capability extremely difficult.
Pompeo noted the enormity of the challenge, but said, "Chairman Kim and I had an opportunity to have a good, sound discussion on [that], so that I think we have a pretty good understanding between our two countries on what the shared objectives are."
Those conversations have also led to some criticism of Pompeo and the embrace he and Trump have made of the dictator, whose horrific human rights record is well documented.
"Our conversations were warm," Pompeo said. He even defended Kim when a reporter asked about his rationality, calling the question "undignified" and noting they had "conversations that involve deep, complex problems, challenges the strategic decision that Chairman Kim has before him."
He also envisioned the two countries coming together in the future: "We had good conversations about the histories of our two nations, the challenges that we've had between us, about the fact that America has often in history had adversaries who we are now close partners with and our hope that we could achieve the same with respect to North Korea."
Pompeo gave a toast at a luncheon in North Korea hosted by senior official Kim Yong Chol, calling the man a great partner in making the summit a success. "For decades, we have been adversaries. Now we are hopeful that we can work together to resolve this conflict," Pompeo said Wednesday.
Critics blast the "warm" words and smiles, while supporters say it is part of diplomacy.
"This administration has been significantly and sufficiently tough on North Korea. I'm proud to stand behind that," acting Under Secretary of State for Public Diplomacy and Public Affairs Heather Nauert told CNN Friday.