South Korean President Moon Jae-in on Thursday said that he will deliver a private message from North Korean leader Kim Jong Un to President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE during next week's United Nations General Assembly meeting, as South Korea and the U.S. continue to pursue the denuclearization of the Korean peninsula.

"There are things that the United States wants us to convey to North Korea, and on the other side there are also things that North Korea wants us to convey to the United States," Moon told reporters in Seoul after returning from a multi-day trip to North Korea to meet with Kim.

"I will faithfully serve that role when I meet President Trump to facilitate dialogue between North Korea and the United States," Moon added, according to The Associated Press.

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The South Korean president did not disclose the contents of the message from Kim, but the North Korean leader pledged to dismantle his nuclear arsenal during meetings with Moon this week, contingent on unspecified reciprocal action by the U.S.

Kim also expressed a desire for a second meeting with Trump, Moon said. The White House said earlier this month that planning for such a summit is underway and is "certainly something we want to take place."

While the Trump administration expressed optimism following a June summit with Kim about the prospects of denuclearization, talks have stalled in recent weeks.

Trump welcomed the latest developments on the Korean peninsula as "very exciting," and on Wednesday told reporters that relations between the U.S. and North Korea had "very much calmed down."

Asked about what actions Kim might expect the U.S. to take to follow through on denuclearizing, Trump said, "We'll see what he's looking at."

"But, in the meantime, we’re talking," he said. "It’s very calm. He’s calm, I’m calm, so we’ll see what happens.”

Secretary of State Mike Pompeo Michael (Mike) Richard PompeoTreasury sanctions individuals, groups tied to Russian malign influence activities Navalny released from hospital after suspected poisoning Overnight Defense: Pentagon redirects pandemic funding to defense contractors | US planning for full Afghanistan withdrawal by May | Anti-Trump GOP group puts ads in military papers MORE said later that he has invited his North Korean counterpart to meet at next week’s U.N. General Assembly, and that the U.S. is pushing for the peninsula to be free of nuclear weapons by 2021.