The North's statement came on Saturday, hours after the U.S. secretary of state wrapped up two days of talks with senior North Korean officials without meeting Kim Jong-un but with commitments for new discussions on denuclearisation and the repatriation of the remains of American soldiers killed during the Korean war.
As part of his talks with North Korea, Pompeo has been seeking the return of remains from the 1950-53 Korean War and officials from the two sides are due to meet next week to discuss details of this.
While Mr Pompeo on Saturday touted "progress on nearly all of the central issues", the North's Foreign Ministry hours later slammed the U.S. for its "deeply regrettable" attitude in making "unilateral and gangster-like" demands.
He added that his two days of talks with senior North Korean officials had "made progress" and included a "detailed and substantive discussion about the next steps towards a fully verified and complete denuclearisation".
Pompeo said his meeting with Kim Yong Chol, a vice chairman of the Central Committee of the Workers' Party of Korea, produced progress and they talked "a great deal" about a potential timeline for the denuclearization process.
Practically, assuaging Kim's security fears could require risky choices for the USA and its North Asian allies, such as rolling back America's nuclear umbrella or pulling back its troops in South Korea.
North Korea's latest comments, which came after Pompeo said talks had made progress, were a reminder of the difficulties that previous US administrations have had negotiating with the reclusive state. It was the first time he had visited North Korea since the Donald Trump-Kim Jong-un summit.
And in a pointed message to North Korea, Graham said the U.S. has more powerful weapons than sanctions to keep the rogue regime in line - if necessary.
"We had expected that the United States side would offer constructive measures that would help build trust based on the spirit of the leaders' summit. we were also thinking about providing reciprocal measures", said the statement, released by an unnamed spokesman and carried by the North's official Korean Central News Agency.
He said the fact that the U.S.is "cooperating - and not fighting" with Vietnam "is proof that when a country decides to create a brighter future for itself alongside the United States, we follow through on American promises".
Pompeo gave assurances that North Korea is still committed to dismantling its nuclear program despite satellite images that appear to show infrastructure improvements to a nuclear facility and the finalizing of a ballistic missile manufacturing site.
'Dealing with North Korea is hard because Kim Jong Un wants it to be hard, ' said Russel, who was assistant secretary of state for East Asian and Pacific Affairs in the Obama administration.
Earlier reports pointed to progress being made between the two countries, with commitments for new discussions on denuclearisation and the repatriation of the remains of American soldiers killed during the Korean War.
Pompeo was in Pyongyang last week to flesh out that deal.
US Secretary of State Mike Pompeo, center, walks through the streets of Hanoi, Vietnam, Sunday, July 8. "Why should the North Koreans make concessions to one of Trump's aides given the president's record of undercutting them?"
He added that talks would be held soon on the destruction of North Korea's missile engine testing facility.
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