SEOUL, Oct. 7 (Xinhua) -- The United States and the Democratic People's Republic of Korea (DPRK) have agreed to hold the second summit between U.S. President Donald Trump and top DPRK leader Kim Jong Un at an earliest possible date, U.S. Secretary of State Mike Pompeo said Sunday.

Pompeo made the remarks during his meeting with South Korean President Moon Jae-in at the presidential complex in Seoul, after visiting Pyongyang earlier in the day and meeting with the DPRK leader, according to the presidential Blue House of South Korea.

The top U.S. diplomat said he and Kim shared view over the holding of the second U.S.-DPRK summit as quickly as possible, while the U.S. and the DPRK sides agreed to continue consultations to determine an exact date and venue for the second Trump-Kim summit.

The first-ever DPRK-U.S. summit was held in Singapore on June 12. Under a joint statement signed by Trump and Kim, the United States would be providing security guarantee to the DPRK in return for Pyongyang's commitment to complete denuclearization of the Korean Peninsula.

During his visit to Pyongyang, Pompeo said that he also discussed the denuclearization measures, which the DPRK takes, and the U.S. government's observation of the measures, while discussing the corresponding measures from the U.S. side to the DPRK actions.

Additional measures for the denuclearization were discussed during the third summit between the leaders of the two Koreas in Pyongyang in September.

Under the joint declaration signed by Moon and Kim, the DPRK said it was willing to continue with additional steps toward denuclearization, such as the permanent dismantlement of its main Yongbyon nuclear facilities if the United States takes corresponding actions.

Pompeo told Moon that the U.S. and the DPRK sides agreed to form each working-level negotiation team to discuss the denuclearization process and schedule for the second U.S.-DPRK summit.

Moon told Pompeo that he hoped a great success of the second U.S.-DPRK summit to be held, vowing to make all possible efforts South Korea can do.

In his introductory remarks, Pompeo said his visit to Pyongyang was very good and he had productive talks in the DPRK, noting that the two countries walked another step forward though there were lots of things left to do.

Pompeo told Moon that it was very important for him to travel to Seoul right after visiting the DPRK as it indicated South Korea having a very important role in denuclearizing the Korean Peninsula.

Moon expressed his hope that Pompeo's visit to the DPRK and the upcoming second summit between Trump and Kim become an opportunity to make an irreversible, decisive progress in the denuclearization and peace process on the peninsula.