Trump said the meeting, which had been due to take place on Thursday in NY, would be rescheduled, and that he still expected to hold a second summit with North Korean leader Kim Jong Un early next year.
The meeting, scheduled for this week in NY, she said, "will reconvene when our respective schedules permit".
The State Department had earlier confirmed that Pompeo would meet Kim Yong Chol, a close aide of Kim, in NY to discuss progress toward a denuclearisation pact and to arrange a second summit following the historic talks between Trump and Kim in June.
But the regime recluse had cooled the atmosphere, threatening last week to resume the development of its nuclear arsenal if the sanctions that are choking its economy were not lifted.
Pompeo described the planned second meeting between U.S. President Donald Trump and DPRK top leader Kim Jong Un as a chance of making a "substantial breakthrough" in the denuclearization on the Korean peninsula.
At a White House press conference, the president said Pompeo's meeting with Kim Yong Chol will be rescheduled.
"I'd love to take the sanctions off, but they have to be responsive too - it's a two-way street", Trump said. But the Blue House would not reveal the reason for the postponement, referring questions to the State Department.
The meeting comes with the two sides at loggerheads almost five months after the summit, in which Trump and Kim pledged to work toward the denuclearization of the Korean peninsula.
When asked about the cancellation on Wednesday, Trump said, "We're going to change it because of trips that are being made".More news: Juventus vs. Manchester United live stream
In addition to Pompeo's talks with his counterpart, the NY meeting in NY was expected to be the first between Trump's special North Korean envoy, Stephen Biegun, and his counterpart, Choe Son Hui.
Pompeo, speaking on Sunday on Fox News, said he was "not worried" about the North Korean demands and insisted there would be "no economic relief until we have achieved our ultimate objective".
A North Korean tourism industry official recently told the Chosun Sinbo that Panmunjom, where Moon and Kim held their first summit in April, is the most popular tourist destination in the North.
But the deal has resulted in few tangible results, other than the USA suspension of some military exercises with South Korea, and North Korea's stated dismantlement of certain nuclear and missile testing sites, which the US says falls short of its expectations.
US officials have said Vietnam's socialist market economy could be an example for North Korea.
Pyongyang has been pushing for a formal declaration to end the 1950-53 Korean War and replace the armistice that stopped the fighting but left the combatants still technically at war.
It was not immediately clear whether Russian Federation was planning a new push to ease sanctions against North Korea.
The latest NY meeting was set to come ahead of a busy season of diplomacy, with Pompeo meeting senior Chinese officials in Washington on Friday.