Pompeo is now in Tokyo.
His rosy outlook was nearly immediately rejected by North Korea's foreign ministry, which called the USA attitude to the talks "regrettable" and accused the United States of making unilateral demands for denuclearization.
He argued instead for both sides to take a series of simultaneous steps as a "shortcut" to a nuclear-free Korean peninsula.
"Nothing could be further from the truth", State Department spokesperson Heather Nauert said in response.
Professor Yang Moo-jin at the University of North Korean Studies in Seoul said Pyongyang wants to separate "US bureaucrats from President Trump, expressing trust in him".
Some US experts on North Korea said the ongoing disputes show the risk of Washington granting premature concessions to Pyongyang.
In the statement calling the U.S. stance "regrettable", the North Korean Foreign Ministry spokesman quoted by KCNA said the USA is unilaterally demanding denuclearisation and trying to postpone discussion of declaring an end to the Korean War.
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"There is perhaps a two-to-three-month window over the summer to do so before Washington will need to return the focus back to maximum pressure", Cronin said, referring to a US -led drive to press North Korea to give up its arms programmes through tough global sanctions, from which Pyongyang has been seeking relief.
Speaking in Tokyo after meeting with his Japanese and South Korean counterparts, Pompeo said Sunday that denuclearization will be hard and that much work remains. Many were surprised when Trump agreed at the summit in Singapore to end joint military exercises with South Korea.
Many experts doubt Kim's sincerity - a nuclear deterrent to United States intervention has always been a strategic goal of his isolated, autocratic regime - and few expect this to be a quick process, even if Washington wants results within a year.
A failure in the talks would amount to an embarrassment for Pompeo, whom Trump tasked with leading the negotiations and who had said repeatedly that Kim Jong Un was ready to commit to something no North Korean government had delivered on in decades.
"North Korea expected Pompeo to bring a concrete proposal for security guarantee but it was disappointed as the U.S. side reiterated the old demand that the North should denuclearise first before the USA gives it anything in return".
The South Korean newspaper Chosun Ilbo, citing unnamed Washington sources, said the "Rocket Man" CD was a gift for Kim Jong Un - a reference to Trump's former habit of insultingly referring to the North Korean as "Little Rocket Man".
"I think we made progress in every element of our discussions", he added.
"There are things that I have to clarify as well", Pompeo responded. He stressed there was still more work to be done in other areas, much of which would be done by working groups that the two sides had set up to deal with specific issues.
Officials from the two sides would meet next week in Panmunjom, on the border between the two Koreas, to discuss the return of the remains of the some 7,000 US soldiers still listed as missing in action since the 1950-53 Korean War.