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SEOUL, Sept. 20 (Xinhua) -- South Korean President Moon Jae-in said Thursday that Kim Jong Un, top leader of the Democratic People's Republic of Korea (DPRK), had expressed his hope to rapidly hold his second summit with U.S. President Donald Trump during the inter-Korean summit in Pyongyang.

Moon made the remarks in his address to the people at the Seoul press center for the Pyongyang summit, which lasted for three days from Tuesday.

Moon noted that Kim also wished U.S. Secretary of State Mike Pompeo visit the DPRK.

Moon expressed his hope for the rapid resumption of the DPRK-U.S. talks, saying conditions were created through the Pyongyang summit to restart the dialogue between the DPRK and the United States.

The DPRK called for Moon to broker talks between Pyongyang and Washington, offering to closely cooperate with South Korea for the peninsula's complete denuclearization, the South Korean president said.

During a phone call before Moon's visit to Pyongyang, Trump called for Moon to play a role as chief negotiator between the DPRK and the United States for the denuclearization negotiations.

Moon was expected to deliver Kim's message to Trump during his scheduled visit to New York next week to attend the UN General Assembly. Moon was slated to hold a separate summit with Trump on the sidelines of the UN General Assembly.

What was discussed between Moon and Kim for the denuclearization but not included in the Pyongyang Declaration will be conveyed to Trump at the South Korea-U.S. summit, the South Korean leader noted.

Moon and Kim signed the Pyongyang Declaration after their summit talks in Pyongyang, agreeing to further steps for the peninsula's denuclearization and concrete measures to end hostile acts near inter-Korean border areas.

Moon said Kim repeatedly confirmed his firm commitment to the peninsula's denuclearization during their talks in Pyongyang. The DPRK leader wished to focus on economic development after completing the denuclearization, Moon noted.

Under the Pyongyang Declaration, the DPRK said it is willing to take additional steps for the denuclearization, such as the permanent destruction of its main Yongbyon nuclear facility, if the United States takes corresponding actions in accordance with the spirit of the June 12 DPRK-U.S. summit agreement.

The Yongbyon nuclear facility in northwestern DPRK is known to house a five-megawatt graphite-moderated reactor, which produces nuclear material necessary for nuclear warheads.

Calling the DPRK's mentioning of the Yongbyon nuclear facility dismantlement an "important, big step," Moon said the permanent dismantlement of the DPRK nukes had the meaning of being verifiable and irreversible.

The DPRK already dismantled its main Punggye-ri nuclear test site and its key Tongchang-ri missile engine test site.

Under the Pyongyang Declaration, the DPRK agreed to allow experts from relevant countries to monitor a permanent closedown of the Tongchang-ri engine test site and missile launch pads.

Touching on the declaration to end the 1950-53 Korean War, Moon said it is a political declaration to end the war and hostile relations that will become a starting point for negotiations on a peace treaty.

The peace treaty, Moon said, will be signed in the final stage of the complete denuclearization. The Korean Peninsula remains in a technical state of war as the Korean War ended with armistice.

Moon said his country aimed to make the war-ending declaration by the end of this year, adding that he will discuss the issue with Trump during the upcoming South Korea-U.S. summit on the sidelines of the UN General Assembly.

Moon and Kim have held summit meetings three times this year, including the ones on April 27 and May 26 each. Kim promised to visit Seoul for the fourth summit with Moon in the near future.

Kim and Trump held the first-ever DPRK-U.S. summit in Singapore on June 12.