President Donald Trump and North Korean leader Kim Jong Un ended their second summit in Hanoi with no deal after Pyongyang demanded a full lifting of sanctions.

Guterres "appreciates the effort that was made in those discussions, regardless of the results, of the outcome that we saw," UN spokesman Stephane Dujarric said.

"Courageous diplomacy has established the foundation to advance sustainable peace and the complete and verifiable denuclearization of the Korean peninsula."

"We all very much hope that these discussions will continue in that direction."

The UN spokesman stressed that world diplomats were clear-eyed about the prospects for a quick deal on dismantling North Korea's nuclear and ballistic missile programs.

"No one, and that includes the secretary-general, ever thought that this process of engaging with the DPRK would be an easy one," said Dujarric.

The leaders walked away with no set plans for a third meeting, though Trump said he hopes to see Kim again soon.

"Basically they wanted the sanctions lifted in their entirety and we couldn't do that," Trump said before leaving Vietnam aboard Air Force One to head back to Washington.

Before the summit, there was talk that there could be a political declaration ending the 1950-53 Korean War which finished technically with an armistice rather than a peace treaty.

There were also hopes Kim could pledge to destroy North Korea's decades-old Yongbyon nuclear complex, which has long been at the heart of Pyongyang's atomic development but remains shrouded in secrecy.