A newly appointed U.S. special representative for North Korea pledged Tuesday, during meetings with South Korean officials in Seoul, to push forward denuclearization on the Korean Peninsula.

"We have some hard work to do, but we also have a tremendous opportunity created" by U.S. President Donald Trump, South Korean President Moon Jae In and North Korean leader Kim Jong Un, Stephen Biegun said at the outset of the talks with South Korea's top nuclear envoy Lee Do Hoon.

(Lee Do Hoon, left, and Stephen Biegun)

"And we need to do everything we can" to make the most of this opportunity, he said, before adding that the U.S. president is looking forward to working with all his counterparts, including Moon, in the process of denuclearization.

Ahead of the meeting in Seoul, the White House said that North Korea has requested in a letter to Trump a second summit meeting, and Washington has begun the planning process.

In the first-ever U.S.-North Korea summit, held between Trump and Kim in Singapore in June, the North Korean leader committed to "complete" denuclearization of the Korean Peninsula.

But Pyongyang has yet to provide a full inventory of nuclear weapons and fissile materials, as Washington has demanded. Citing a lack of progress in denuclearization talks, Trump canceled Secretary of State Mike Pompeo's planned visit to Pyongyang in late August.

Last week, however, Kim told visiting South Korean officials that he hopes to achieve denuclearization before Trump's first term ends in January 2021.

Ahead of the talks with Lee, Biegun also met with South Korean Foreign Minister Kang Kyung Hwa to exchange ideas on North Korea.

Kang asked the U.S. envoy to play a role in achieving complete denuclearization and a peace settlement on the peninsula, to which Biegun responded by saying he will do his best in cooperation with Seoul, according to the South Korean Foreign Ministry.

(Biegun, left, and Kang Kyung Wha)

"We had in-depth discussions on how to proceed with denuclearization in the current situation and how to achieve a peace settlement on the Korean Peninsula," Lee told reporters after meeting with Biegun.

Lee added that he will keep in close contact with the U.S. envoy so the two sides remain on the same page and cooperate to the maximum extent possible.

At the start of a separate meeting later Tuesday, Biegun told Unification Minister Cho Myoung Gyon that the United States and South Korea "need to find a pathway to a future here on the Korean Peninsula that allows inter-Korean relations to deepen as much as possible."

After South Korea, Biegun is scheduled to visit China and Japan for talks with officials in those countries on ways to achieve North Korean denuclearization, according to the U.S. State Department.

The former Ford Motor executive was named special representative for North Korea last month. He was supposed to accompany Pompeo to Pyongyang until that trip was nixed by Trump.

Moon and Kim are set to meet in Pyongyang on Sept. 18-20 for their third summit, following ones in April and May, both of which were held in the truce village of Panmunjeom.

At a meeting Tuesday with government officials, Moon said what is now needed is "not another joint declaration but stable improvement in inter-Korean relationships." Thus Moon said he will pursue in particular at next week's summit the easing of military tension between the Koreas, and North Korea and the United States.

Moon also called for the leaders of the United States and North Korea to make "bold decisions" to take the denuclearization process to a higher level, and vowed that Seoul will continue to play the role of mediator between Washington and Pyongyang.