A failure in the talks would amount to an embarrassment for Pompeo, whom Trump tasked with leading the negotiations and who had said repeatedly that Kim Jong Un was ready to commit to something no North Korean government had delivered on in decades.
After the historic U.S.
Speaking privately, U.S. officials suggested the harshly-worded North Korean reaction was a negotiating tactic.
"We still cherish our good faith in President Trump", the spokesman said, while warning against repeating past failures.
A US State Department spokeswoman said the two sides have set up working groups to deal with "nitty gritty stuff" including validation of efforts to achieve denuclearisation.
Just hours after Pompeo left the North Korean capital and described the negotiations as "productive", North Korea's Foreign Ministry released a scathing statement that cast the entire endeavor in doubt.
While the secretary told reporters that progress was made "on nearly all of the central issues" and involved "good-faith negotiations", North Korea said the USA attitude, demanding denuclearisation, was "regrettable".
"We thought that the U.S. side would come with a constructive proposal which accords with the spirit of the DPRK-U.S. summit meeting and talks".
It said the outcome of the follow-up talks was "very concerning" because it has led to a "dangerous phase that might rattle our willingness for denuclearization that had been firm". "Our expectations and hopes were so naive it could be called foolish".
"It's certainly a setback and a change of heart and a very different picture coming from the North Korean side".
At that meeting, Trump lavished praise on Kim and agreed to suspend America's joint military exercises with South Korea in the region.
Mr Trump had dubbed Mr Kim "Rocket Man" previous year, in reference to repeated North Korean missile tests.
"There are things that I have to clarify as well", Pompeo responded.
Before he left Pyongyang, Pompeo said U.S. negotiators and their North Korean counterparts discussed the idea of a full declaration of North Korean weapons of mass destruction stockpiles, and setting a timeline for giving them up.
The statement from Pyongyang Saturday raises significant questions about North Korea's commitment to denuclearize - something Trump suggested was a done deal. But he maintained that progress is being made.
"Pompeo appears to have presented the North Koreans with some demands and requirements for real moves towards denuclearization, as opposed to the symbolic steps and empty language Pyongyang has been using so far". "And when you want it bad, you get it bad".
"This is classic North Korean negotiating tactics: Pocket concessions from the United States while stringing our discussions on their own commitments", said Abraham Denmark, a senior defence official for East Asia under former President Barack Obama.
Bruce Klingner, a former Central Intelligence Agency analyst and now an Asia expert at the Heritage Foundation, said in an email that "it appears Trump took his victory lap a tad too soon". How the USA will respond publicly remains to be seen, as so far the administration doesn't appear willing to even acknowledge that the talks went badly this time around.
Pompeo actually corrected him to say that he did sleep well: "Director Kim, I slept just fine".
Pompeo sought to dispel suggestions that the Trump administration has backed down from demanding the complete, verifiable and irreversible dismantlement of the North's nuclear weapons.