The diplomacy on North Korea has seen a series of fits and starts, with Trump at one point scrapping a trip by Pompeo just as he was set to fly to Pyongyang.
Nauert said the United States remained focussed on fulfilling the commitments agreed to by President Donald Trump and North Korean leader Kim Jong-un at the Singapore summit in June, reported The Washington Post.
North Korea has long sought USA recognition as a nuclear state and guarantees for the survival of the generational Kim regime, which human rights groups consider one of the most repressive in the world.
Pompeo had been due to hold talks in NY on Thursday with senior North Korean official Kim Yong Chol aimed at paving the way for a second summit between Trump and Kim Jong Un and at making progress on denuclearization.
North Korea is getting increasingly angry at the USA, as talks are deadlocked and tensions between the two countries are on the rise, a source familiar with the discussions told CNN.
Trump, in a free-wheeling news conference after midterm elections, said he was willing eventually to ease the pressure on North Korea.
"It is hard for us to comment on Chairman Dunford's remarks, because we don't know exactly what he meant by it", presidential spokesperson Kim Eui-kyeom said in a regular press briefing on Tuesday.
"Dunford is not talking about things that are going to happen immediately, but brought up issues that will be discussed inevitably", said Shin Beom-chul, a senior researcher at the Asan Institute, a Seoul-based security think tank.
The cancellation comes amid North Korean threats to restart its nuclear development unless the USA begins to remove sanctions - a step the administration says it will not take until North Korea meaningfully moves to denuclearize, which it so far has not done.
US President Donald Trump said Wednesday that he expects to meet North Korean leader Kim Jong-un "sometime early next year".
At the news conference, Trump pointed out that North Korea has not tested further missiles amid the talks.
The statement did not threaten to end nuclear negotiations, however, and the North Koreans are said to still be pursuing a second summit between President Trump and Kim Jong Un.
"Gen. Dunford was simply highlighting that the Defense Department is in support of the State Department when it comes to the ongoing diplomatic negotiations with North Korea", JCS spokesperson Col. Patrick S. Ryder told Voice of America.
But the growing divide between the USA and South Korea also has many concerned, as liberal President Moon Jae-in pushes for closer Korean ties including demilitarizing the border and increasing economic cooperation.
Pompeo, speaking 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". "But we are very happy how it is going with North Korea", Trump said.
"It's a lot easier when the North Koreans are misbehaving, that tends to promote solidarity between Washington and Seoul", Russel said.