U.S. President Donald Trump said Monday he will have a second summit with North Korean leader Kim Jong Un "in the not too distant future" in an effort to denuclearize the country.

"The location is being worked on, the time is being worked on, we'll be announcing it," Trump told reporters after a meeting with South Korean President Moon Jae In in New York.

Trump and Moon met after the South Korean leader held a summit last week in Pyongyang with Kim, who expressed willingness to have a second meeting with Trump soon to push ahead with denuclearization negotiations.

(Getty/Kyodo)

Moon told Trump that Kim reaffirmed his commitment to denuclearization, and that Kim's "decision to relinquish its nuclear program has been officialized to a degree that not even those within North Korea can reverse."

"Chairman Kim also repeatedly conveyed his unwavering trust and expectations for you, while expressing his hope to meet you soon to swiftly conclude the denuclearization process with you, because you are, indeed, the only person who can solve this problem," Moon told Trump at the meeting, part of which was open to the media.

Kim is chairman of the North's ruling party, the Workers' Party of Korea.

Earlier Monday, U.S. Secretary of State Mike Pompeo expressed eagerness to travel to North Korea "before the end of the year" to make "final preparations" for a second summit, which would follow a historic first meeting between Trump and Kim in June in Singapore.

During two-day talks through last Wednesday with Moon in Pyongyang, Kim pledged to permanently dismantle North Korea's key missile test site in Tongchang-ri under the watch of international experts, and to do the same to its main nuclear complex in Yongbyon if the United States takes reciprocal measures.

Moon's trip to the North was intended to break the impasse over U.S.-North Korea negotiations on Pyongyang's abandonment of its nuclear and missile programs.

The talks began after Kim committed to "complete" denuclearization of the Korean Peninsula in the first-ever U.S.-North Korea summit.

The United States has criticized North Korea for failing to take credible measures to give up its nuclear weapons program. Pyongyang has insisted it first wants a declaration on ending the Korean War as a way of building trust and guaranteeing its security.

The 1950-1953 conflict -- involving the U.S.-led United Nations Command on one side and North Korean and Chinese forces on the other -- ended in an armistice, not a peace treaty.

After the latest inter-Korean summit, Pompeo expressed readiness to "immediately" engage in negotiations with North Korea in a bid to achieve the goal of denuclearizing Pyongyang by the end of Trump's first term in January 2021.

As part of efforts to jump-start stalled denuclearization talks, Pompeo said he invited North Korean Foreign Minister Ri Yong Ho to meet while in New York for the U.N. General Assembly.

Aside from North Korea, Trump and Moon on Monday welcomed the conclusion of negotiations to revise the U.S.-South Korea free trade agreement.

"The new U.S.-Korea agreement includes significant improvements to reduce our trade deficit and to expand opportunities to export American products to South Korea," Trump said.

"These outcomes give the finest American-made automobiles, innovative medicines and agricultural crops much better access to Korean markets," he said.

Under the revised FTA, South Korea will double the annual number of American automobiles that can enter its market using U.S. safety standards without further modifications from 25,000 to 50,000 per manufacturer a year, according to the White House.