US Secretary of State Mike Pompeo has said he expects North Korea's leader will live up to his commitment not to resume nuclear and missile tests.
Mr Pompeo said Kim Jong-un had promised US President Donald Trump in Vietnam that testing would not resume.
His comments follow a suggestion by North Korean-Vice Foreign Minister Choe Sun-hui that denuclearisation talks might end and testing could resume.
The US says sanctions will remain until Pyongyang destroys all nuclear sites.
Mr Pompeo told reporters on Friday that "on multiple occasions [Mr Kim] spoke directly to the president and made a commitment that he would not resume nuclear testing, nor would he resume missile testing" during their February summit.
"That's Chairman Kim's word," Mr Pompeo said. "We have every expectation that he will live up to that commitment."
Earlier, Ms Choe said US diplomats had thrown away "a golden opportunity" during the summit when North Korea offered to dismantle its main Yongbyon nuclear complex.
Talks in Hanoi collapsed when Mr Trump refused to lift any sanctions until North Korea was completely denuclearised.
But Mr Pompeo said he is "hopeful" that discussions will continue.
"I saw the remarks [Ms Choe] made - she left open the possibility negotiations would continue. It's the administration's desire that we continue to have conversations around this."
What did North Korea say?
Ms Choe said in Pyongyang that Mr Kim would decide whether to stick to the launch and test moratorium, and she expects him to "clarify his position" soon.
"We have no intention to yield to the US demands in any form, nor are we willing to engage in negotiations of this kind," she told reporters in North Korea, Russia's state Tass news agency reported.
She accused the US of taking a "gangster-like" stance, according to the Associated Press, but added that "personal relations between the two supreme leaders are still good and the chemistry is mysteriously wonderful".
Ms Choe said that North Korea's demand during the recent summit was for five key economic sanctions to be lifted, not all sanctions, as Mr Trump said after talks broke down.
"What is clear is that the US has thrown away a golden opportunity this time," she said. "I'm not sure why the US came out with this different description. We never asked for the removal of sanctions in their entirety."
What was the US position?
Mr Trump and Mr Pompeo clearly stated after last month's talks that North Korean officials had asked for full sanctions relief.
"It was all about the sanctions. They wanted the sanctions lifted in their entirety and we couldn't do that," Mr Trump told reporters. "Sometimes you have to walk and this was one of those times," he said.
In Washington this week, the US special representative for North Korea, Stephen Biegun, said that diplomacy was "still very much alive", though he did not say if there had been any negotiations since the summit, or outline any plans for further talks.
The two leaders first met in Singapore last year, in an unprecedented summit between a US sitting president and a North Korean leader. Their second meeting was in Hanoi in February.
At a news conference after the second summit, Mr Trump said no plans had been made for a third summit, but he expressed optimism about a "good outcome" in the future.
Door to diplomacy still open
Laure Bicker, BBC Seoul correspondent
So does this mean a return to "fire and fury"? Not quite. North Korea's tactic might be to hope this will initiate a reaction from the US. Pyongyang is aware that Donald Trump has boasted about his ability to get Mr Kim to stop firing missiles and testing nuclear missiles.
"As long as there's no testing," said Mr Trump, "I'm in no rush."
After the two leaders failed to secure a deal in Hanoi, and with economic sanctions still in place, North Korea might be trying to hurry the US president along and get him back to the table with a better deal.
It is worth noting Choe Sun-hui still praised the personal relationship between Kim Jong-un and Donald Trump. So the door to diplomacy is still open. Instead she blamed Mike Pompeo and National Security Adviser John Bolton for hardening the US position.
North Korea also has hardliners of its own, who may perceive Kim Jong-un's 120-hour train trip to Hanoi and back as a failure. This announcement lets them know, along with the Trump administration, that Mr Kim is standing firm.