Mr Pompeo also sought to dispel suggestions the Trump administration had backed down from demanding the complete, verifiable and irreversible dismantlement of the North's nuclear weapons. But after two days of theatrical amity in Pyongyang it illustrated the gulf that remains between the two sides.
Pompeo was in North Korea over the weekend meeting with officials, not Kim himself, to discuss the return of the remains of US soldiers who were killed in the Korean War and to further press for the dismantling of a North Korean missile engine test site.
Pompeo visited the Communist country for the third time on Friday - the first following the historic summit between its leader, Kim Jong Un, and President Trump in May - in an effort to encourage Pyongyang to get rid of its nuclear weapons, which received a chilly response from North Korean officials.
"The media narrative which I really disagree with is that the Singapore summit declaration deemed that North Korea would stop everything it was doing [regarding nuclear weapons development] right away".
Pompeo downplayed the "gangster" accusations at a press conference in Tokyo with the foreign ministers of South Korea and Japan.
"And so if those requests were 'gangster-like, '" Pompeo added, "then the world is a gangster because there was a unanimous decision at the U.N. Security Council about what needs to be achieved". "But Washington should not allow nuclear talks to be held hostage to peace talks or else there could be peace with a nuclear-armed North Korea indefinitely".
"In light of the once-unimaginable prosperity and partnership we have with Vietnam today", Pompeo said, "I have a message for Chairman Kim Jong Un: President Trump believes your country can replicate this path".
But while Pompeo on Saturday painted a positive picture of the follow-up talks, North Korean officials accused the USA of trying to unilaterally pressure their country into abandoning its nuclear programme.
The rhetoric issued by North Korea following the Pompeo meetings showed a return to sharp, provocative language, dangling the possibility of war if the USA continued to make demands.
"It seems the U.S. misunderstood our goodwill and patience", the statement said. "But this expectation and hope of ours was so naive as to be gullible", the statement said.
Pompeo said he had pushed North Korea on a promise to destroy a missile engine test site.
After two days of talks with senior officials, he said efforts to push Pyongyang towards abandoning nuclear weapons had global backing.
And Pompeo was adamant that those further negotiations would go ahead.
In his first remarks about the challenging weekend talks, Trump suggested that China, North Korea's chief ally, might be interfering in reaction to the Trump administration's stance on US-China trade.
"President Trump is clearly telegraphing to the North Koreans that there's distance between China and the United States ... and the North Koreans are going to use that to their advantage", said Joel Wit, a senior fellow at the Stimson Centre, a Washington-based think tank, and founder of 38 North, a website focused on North Korea issues.