Thomas Maresca | Special to USA TODAY

USA TODAY

Handout, Getty Images

SEOUL, South Korea — South Korean President Moon Jae-in said on Sunday that Kim Jong Un expressed a firm commitment to complete denuclearization of the Korean Peninsula and that the North Korean leader still wants to meet with President Trump.

Meanwhile, Trump said Saturday night that talks on salvaging the summit meeting were "going along very well."

Moon briefed reporters on his surprise Saturday meeting with Kim, which took place at the Panmunjom border village inside the Demilitarized Zone that divides the Korean Peninsula.

The meeting came a month after the first inter-Korean summit between the two leaders. Moon said that the casual nature of their second meeting was “like a normal routine between friends.”

Moon said that he urged North Korea and the U.S. to directly communicate to avoid misunderstandings, and that Kim agreed.

Trump, speaking from the Oval Office while greeting an American freed from Venezuela, said "we’re doing very well in terms of the summit with North Korea," adding that “there are meetings going on as we speak."

On Thursday, Trump canceled a June 12 North Korea-U.S. summit that had been scheduled to be held in Singapore, citing the “tremendous anger and open hostility” of recent communications from Pyongyang. However, Trump has left the door open since, tweeting on Friday that Washington was having “very productive talks with North Korea” about reinstating the summit.

Moon told reporters that working-level talks between the U.S. and North Korea were going to happen soon and he that he was “looking forward to the June 12 meeting.”

"We agreed that the June 12 US-North Korea summit must be successful," Moon said of his meeting with Kim.

In a statement released before Moon’s briefing on Sunday, North Korean state news agency KCNA said that Kim Jong Un “expressed his fixed will” to hold the summit with the U.S.

Moon also said that he hoped to hold three-way talks with the U.S. and North Korea to discuss a formal peace treaty to end the Korean War, which ceased in 1953 with an armistice, after a successful Trump-Kim summit.

On Saturday, Trump complained on Twitter about a New York Times story that said administration officials disagreed on how to handle North Korea. The piece quoted an anonymous source saying it's too late to hold the meeting on June 12.

"WRONG AGAIN!" Trump tweeted.

South Korea, which brokered the talks between Washington and Pyongyang, was caught off guard by Trump’s abrupt cancellation of the Kim summit.

Moon said Trump’s decision left him “perplexed” and was “very regrettable.” He urged Washington and Pyongyang to resolve their differences through “more direct and closer dialogue between their leaders.”

North Korea issued an unusually restrained and diplomatic response to Trump, saying it’s still willing to sit for talks with the United States “at any time, (in) any format.”

“The first meeting would not solve all, but solving even one at a time in a phased way would make the relations get better rather than making them get worse,” North Korean Vice Foreign Minister Kim Kye Gwan said in a statement carried by Pyongyang’s official Korean Central News Agency (KCNA).

Notably, the statement did not appear in Saturday’s edition of Rodong Sinmun, the official mouthpiece of the North’s ruling party that’s widely read by North Koreans.

The newspaper instead focused on Kim's visit to the coastal town of Wonsan to inspect the construction of a beachfront tourist complex. Kim ordered the complex to be finished by April 15 next year to mark the birthday of his late grandfather and North Korea founder Kim Il Sung. Kim's comments published by the newspaper did not include any mention of his potential meeting with Trump.