President Moon Jae-in on Friday hailed the agreed-upon summit between US President Donald Trump and North Korean leader Kim Jong-un as a "historic milestone" for peace on the Korean Peninsula.

Moon made the remark through his spokesman Kim Eui-kyeom after Trump agreed to meet with the North's leader by May, accepting Kim's offer to meet as soon as possible. The envisioned meeting would be the first-ever between leaders of the two Cold War foes.

"The May meeting will be recorded as a historic milestone that realized peace on the Korean Peninsula," Moon said. "If President Trump and Chairman Kim meet following an inter-Korean summit, complete denuclearization of the Korean Peninsula will be put on the right track in earnest."

Moon also said he extends gratitude to Trump and Kim for their "courage and wisdom."

"In particular, the leadership of President Trump, who gladly accepted Chairman Kim's invitation, will receive praise not only from people in the South and the North but also from people around the world who wish for peace," Moon said.

"Our government will carefully handle this opportunity that came like a miracle," he said. "We will move things in a way that is faithful and careful but is not slow."

Moon also said he is grateful to other world leaders for their attention and interest in the issue.

In Washington earlier, South Korea's presidential national security adviser, Chung Eui-yong, conveyed the North Korean leader's meeting proposal to Trump while briefing Trump on the results of his meeting with the North's leader in Pyongyang on Monday.

During the briefing to Trump, Chung also quoted the North's leader as saying, "I will be able to produce a big outcome if I meet and talk to President Donald Trump," according to the presidential spokesman.

Chung also told Trump that Kim talked candidly and that he could sense Kim's sincerity.

"Of course, we have to make sure not to repeat the mistakes of the past, but I hope the US will accept our judgment about Chairman Kim and not miss this opportunity. Chairman Kim wants to meet with President Trump as early as possible," Chung was quoted as telling Trump.

Chung also said Trump has been of big help and South Korea highly appreciates his role. Chung also told Trump that Moon offered words of appreciation to him before thousands of people during a national prayer breakfast earlier this week, according to the spokesman.

After learning of Kim's invitation, Trump immediately accepted the offer, the spokesman said.

Trump was also quoted as saying that he highly appreciates South Korea's role, and said, while looking at aides around him, that talking is a good thing.

Trump then asked the South Korean officials to announce what was discussed at the White House. The South Korean officials accepted the request and worked with US National Security Council officials for the next two hours to put together a statement to be announced, according to the spokesman.

"It was such a sudden request that Chung couldn't even report it to President Moon," spokesman Kim said. "It was only after completing the announcement's wording that Chung called President Moon via a security line linking Cheong Wa Dae to the White House and reported about the announcement's wording."

Chung's meeting with Trump began around 4:15 p.m. Thursday (Washington time) and lasted 45 minutes.

Also in attendance were about a dozen US officials, including Vice President Mike Pence, Defense Secretary Jim Mattis, Director of National Intelligence Dan Coats, White House chief of staff John Kelly, Joint Chief of Staff Chairman Joseph Dunford, National Security Advisor H.R. McMaster, Deputy Secretary of State John Sullivan and CIA Deputy Director Gina Haskell.

Other South Korean officials present at the meeting were Suh Hoon, director of the National Intelligence Service, and South Korean Ambassador to the US Cho Yoon-je.

Before the meeting with Trump, Chung met with McMaster and Suh also met one-on-one with Haskell for about half an hour before the four held a joint meeting for about an hour.

Spokesman Kim said that the South Korean officials were expected to meet with Trump on Friday (local time), but Trump asked for an earlier meeting.

Kim also said that the South Korean officials stayed at the White House for about five hours.

Meanwhile, Kim said that Moon ordered the formation of a preparatory committee for a summit with the North, set for late April, and named his chief of staff, Im Jong-seok, to chair the committee.

"The key mission of the preparatory committee is to produce a substantial agreement at the April summit," the spokesman said, adding that members of the committee will also take part in high-level meetings with the North to set up the summit. (Yonhap)