"I expect we'll make some real progress, including an effort to make sure that the summit between our two leaders can take place where we can make substantial steps toward denuclearization," Pompeo said on CBS's "Face the Nation."
Pompeo's meeting with Kim Yong Chol later this week comes with the two sides at loggerheads nearly five months after a historic summit in June in which Trump and Kim pledged to work toward the denuclearization of the Korean peninsula.
North Korea's foreign ministry warned earlier in the week that Pyongyang will "seriously" consider reviving its nuclear weapons program unless US sanctions are lifted.
Pompeo dismissed the statement, telling "Fox News Sunday," "I'm not worried about that."
North Korea says 'completely' dismantled nuclear test site
"We are very focused. We know with whom we are negotiating, we know what their positions (are) and President Trump has made his position very clear," Pompeo said.
He added that there would be "no economic relief until we have achieved our ultimate objective."
News of the meeting, and the possibility of another summit, also comes just two days before crucial US midterm elections seen as a referendum on Trump.
Trump has often pointed to the detente with North Korea — the subject of sabre-rattling rhetoric and soaring tensions early in his term — as a signature foreign policy accomplishment.
Pompeo emphasised in both television appearances that there have been no missile or nuclear tests since the summit in Singapore, and remains of US troops killed during the Korean War have been returned.
"We've had success in just a handful of months since this past June, and we continue to make good progress. I'm confident that we'll advance the ball again this week when I'm in New York City," he said on CBS.
But the progress has fallen well short of the promise of the summit, with Washington pushing to maintain sanctions against the North until its "final, fully verified denuclearization," and Pyongyang condemning US demands as "gangster-like."
North Korea criticises 'alarming' US impatience on denuclearisation
"The improvement of relations and sanctions are incompatible," said the foreign ministry statement, released under the name of the director of the foreign ministry's Institute for American Studies.
"What remains to be done is the US corresponding reply," it added.
Kim Yong Chol, Pompeo's counterpart in the talks, is a general, a former top intelligence chief and right-hand man to the North Korean leader.
He visited the White House in the diplomatic run-up to the Singapore summit, and has been Pompeo's chief interlocutor in the months since.
In mid-October, Pompeo evoked the possibility of a second summit, preceded by talks with Kim Yong Chol.
"We're working on finding dates and times and places that will work for each of the two leaders," Pompeo said at the time.
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