North Korean leader Kim Jong Un is committed to "complete" denuclearization of the Korean peninsula and to a landmark summit with U.S. President Donald Trump, South Korea's leader said Sunday, as Trump announced that plans for the meeting are moving along "very nicely."

The U.S. State Department said Sunday a U.S. delegation was holding talks with North Korean officials at a border truce village.

"A U.S. delegation is in ongoing talks with North Korean officials at Panmunjom," State Department spokeswoman Heather Nauert said in a statement. "We continue to prepare for a meeting between the President and North Korean leader Kim Jong Un."

The latest conciliatory declarations capped a turbulent few days of diplomatic brinkmanship that had sent tensions soaring.

Trump rattled a saber on Thursday by canceling the planned June 12 meeting with Kim in Singapore, citing "open hostility" from Pyongyang.

But within 24 hours he reversed course, saying it could still go ahead after productive talks were held with North Korean officials.

"It's moving along very nicely," Trump told reporters when asked for an update. "We're looking at June 12 in Singapore. That hasn't changed."

Trump's unpredictability sparked a surprise meeting on Saturday between Kim and South Korean President Moon Jae-in -- only the fourth time leaders from the two countries have ever met -- as they scrambled to get the talks back on track.

Pictures showed them shaking hands and embracing on the North Korean side of the Demilitarized Zone separating the two nations.

Moon said Kim reached out to him to arrange the hasty meeting "without any formality," a stunning development given that the Koreas only reopened a defunct hotline between the two nations last month.

The North Korean leader described the Singapore summit as a landmark opportunity to end decades of confrontation.

"He... expressed his intention to put an end to the history of war and confrontation through the success of the North-U.S. summit and to cooperate for peace and prosperity," Moon told reporters on Sunday.

Moon added that Kim reaffirmed his commitment to "complete denuclearization" but was uncertain "whether he could trust that the U.S. would end its hostile policy and guarantee the security of his regime" if he gave up those weapons.

Pyongyang's state-run KCNA news agency said Kim "expressed his fixed will" to meet Trump, adding South and North Korea would hold another round of "high-level" talks on June 1.

There was a further signal of progress Saturday as White House press secretary Sarah Sanders confirmed a team of U.S. officials was leaving for Singapore "in order to prepare should the summit take place."

Trump's original decision to abandon the summit initially blindsided South Korea, which had been brokering a remarkable detente between Washington and Pyongyang in a desperate bid to avoid a devastating conflict.

Last year Trump and Kim were trading war threats and insults after Pyongyang tested its most powerful nuclear weapon to date and missiles which it said were capable of reaching the U.S. mainland.

Tensions were calmed after Kim extended an olive branch by offering to send a delegation to the Winter Olympics in South Korea, sparking a rapid detente that led to Trump agreeing to hold direct talks with Pyongyang.

But the flurry of diplomatic backslapping and bonhomie disappeared in recent weeks with increasingly bellicose rhetoric from both top US administration officials and Pyongyang.

There are still stark differences between what the two sides hope to achieve.

Washington wants North Korea to give up all its nukes in a verifiable way as quickly as possible in return for sanctions and economic relief.

Pyongyang has a different view of what denuclearization might look like and remains deeply worried that abandoning its deterrent would leave the country vulnerable to regime change.

Saturday's meeting between Moon and Kim took place on the North Korean side of Panmunjom, a village that straddles the border between the two countries, where the 1953 armistice was signed.

The two leaders had met in the same village only last month.

Kim Yong-hyun, professor of North Korea studies at Dongguk University in Seoul, said Moon and Kim moved quickly to defuse the crisis after Trump's shock cancellation.

"Moon essentially helped relay messages from Trump to Kim and vice versa, to further smooth the process and to resume negotiations," he told AFP, saying the Singapore meeting was "clearly back on track."

In Seoul Sunday most people whom AFP spoke to appeared to welcome Moon's move to talk to Kim.

"I think it was a good thing if meeting in person and having a direct conversation about each other's intentions helps us proceed to the next step," said Lee Tae-kyoung.

Unlike last month's summit, which was held in front of live TV cameras, Saturday's meeting took place in utmost secrecy, with reporters only told later that it had taken place.

Footage released by the Blue House on Twitter, accompanied by a dramatic orchestral score, showed Moon arriving in a convoy of cars and first shaking hands with Kim's sister Kim Yo Jong, who has played a major public role in recent talks with the South.