"I think he [Guterres] very much appreciates the effort that was made in those discussions regardless of the results, of the outcome that we saw", Dujarric said. "We all very much hope that these discussions will continue".
The spokesman added that Guterres did not expect that the process of engaging with the North Korean government will be an easy one.
US President Donald Trump and the North Korean leader Kim Jong-un had a two-day summit in the Vietnamese capital of Hanoi. Trump said he decided to walk away from the summit after Kim demanded full sanctions relief.
The two were expected to make at least some progress in denuclearization talks. The meeting on Thursday was to end in an agreement signing ceremony, according to the White House schedule, but it was scrapped after the talks wrapped up more than an hour early.
The minister said Washington had insisted that Pyongyang make "one more" step beyond the dismantlement of the Yongbyon facility, adding that North Korea's position on nuclear disarmament deal would not change even if Washington sought further talks.
Meanwhile, Members of the United States Congress called Thursday on the Trump administration to step up sanctions on North Korea after the second summit between the two countries.
"I hope that the Administration will continue to talk to the North Koreans. I also hope we will increase sanctions enforcement and build a stronger sanctions regime", US Congressman Brad Sherman Sherman, a member of the House Foreign Affairs Committee, said in a press release.
Senator Cory Gardner agreed that the Trump administration must not offer any kind of normalization without denuclearization, calling for full sanctions, a robust military posture and the international isolation of North Korea in coordination with US allies and partners.
At the first historic summit, held in Singapore in June 2018, Trump and Kim agreed that Pyongyang would make steps toward denuclearization in exchange for the potential removal of sanctions and the freezing of US and South Korean military drills.