While Pompeo offered a relatively positive assessment of his meetings, North Korea's Foreign Ministry said in a statement that the USA betrayed the spirit of last month's summit between President Donald Trump and Kim by making "unilateral and gangster-like" demands on "CVID", or the complete, verifiable and irreversible denuclearization of North Korea.
Pompeo reiterated in Tokyo on Sunday that sanctions on North Korea will remain in place until Pyongyang achieves "final" denuclearization.
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 roughly 7,000 US soldiers missing since the 1950-1953 Korean War.
But as he arrived in Tokyo to brief his Japanese and South Korean counterparts, his North Korean hosts issued an angry statement rejecting his efforts and appealing to US President Donald Trump to revive the peace process.
U.S. Secretary of State Mike Pompeo on Saturday said the Trump administration considered the meeting "very important" as the "first senior-level face-to-face meeting" between Pyongyang and Washington since June's DPRK-U.S. summit.
Calling for a "phased and synchronous approach", the statement added: "This is incomparable with the irreversible step taken by (North Korea) to explode and dismantle the nuclear test ground".
As Mr. Pompeo departed Pyongyang, he told reporter that the talks achieved progress "on nearly all of the central issues" in the talks, including on setting a timeline for its denuclearisation, though more work remained to be done. "It can be your miracle in North Korea as well", Mr Pompeo said. They buy $100 billion from us. "The U.S. should make a serious consideration of whether the toleration of the headwind against the wills of the two top leaders would meet the aspirations and expectations of the world people as well as the interests of its country", the statement concluded.
Pompeo added that the USA and world powers would maintain economic sanctions against North Korea until full denuclearization was achieved.
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He added that the United States also has to partner with Turkey to maintain a US troop presence in northeastern Syria to ward off Iran.
He admitted "there's still more work to be done" in other areas.
Pompeo spoke after North Korea said the talks "brought us in a risky situation where we may be shaken in our unshakable will for denuclearization, rather than consolidating trust".
Now, three weeks later, the two sides were still at odds on all issues, including exactly what denuclearization means and how it might be verified, after a third visit to Pyongyang by U.S. Secretary of State Mike Pompeo.
U.S. State Department spokesperson Heather Nauert tweeted that Pompeo spoke briefly before leaving Pyongyang.
"Kim can afford to play hardball because it's clear to him that Trump, who has already told Americans they can sleep soundly because the threat is now over, badly wants a deal", Russel said.
The criticism, published on North Korea's government-run Uriminzokkiri website, said Washington should stop provoking the North with an "anachronistic human rights racket' at a time of diplomatic attempts to improve ties".
Today's meeting follows three hours of talks at the Baekhwawon state guest house in Pyongyang on Friday, following the USA delegation's arrival in Pyongyang just before noon.