In this photo provided by the government of the Democratic People's Republic of Korea (DPRK), DPRK leader Kim Jong-un, center left, and US Secretary of State Mike Pompeo walk together before their meeting in Pyongyang, Oct 7, 2018. (KOREAN CENTRAL NEWS AGENCY/KOREA NEWS SERVICE VIA AP)

BEIJING – The Democratic People's Republic of Korea (DPRK) and the United States agreed Sunday to hold further negotiations for a second DPRK-US summit as quickly as possible.

During his visit to Pyongyang on Sunday, US Secretary of State Mike Pompeo held "productive" discussions with the DPRK top leader Kim Jong-un, according to a report by the DPRK's state-run news agency KCNA.

There was an agreement on the issue of holding the working negotiation for the second DPRK-US summit talks as early as possible, and relevant procedure-related issues and ways were also discussed. 

Korean Central News Agency

The top US diplomat said he and Kim shared the same view over holding a second US-DPRK summit as quickly as possible, while the US and the DPRK sides agreed to continue consultations to determine an exact date and venue for the second summit between the DPRK leader and US President Donald Trump.

Pompeo and Kim also agreed to instruct their respective working-level teams to meet soon to intensify discussions on the key outstanding issues related to the Singapore Summit Joint Statement, said State Department spokesperson Heather Nauert in a statement.

READ MORE: Pompeo, Kim held 'productive' talks on S'pore pact, says US

Kim also invited inspectors to visit the Punggye Ri nuclear test site to confirm that it has been irreversibly dismantled, the statement said.

"President Trump looks forward to continuing to build upon the trust established with Chairman Kim in Singapore and anticipates meeting again soon," it added.

"I look forward to seeing Chairman Kim again, in the near future," US President Donald Trump twitted shortly after Pompeo left the DPRK.

Progress is being made in implementing the June 12 joint statement agreed upon at the first DPRK-US summit held in Singapore, said Kim, expressing his gratitude to Trump for making a sincere effort to this end, according to the KCNA.

"Kim Jong-un expressed satisfaction over the productive and wonderful talks with Mike Pompeo at which mutual positions were fully understood and opinions exchanged," said the KCNA report.

Kim also "expressed his will and conviction that great progress would surely be made in solving the issues of utmost concern in the world" in the projected second DPRK-US summit talks.

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Pompeo said that both leaders believe there is real, substantive progress that can be made at the next summit.

"What we all hope will be the denuclearization and the change in the relationship here on the peninsula ... I'm confident together we can achieve the outcome that the world so desperately needs," he noted.

In this photo provided by the DPRK government, DPRK leader Kim Jong-un and US Secretary of State Mike Pompeo, back center left, have a luncheon at a state guesthouse in Pyongyang, Oct 7, 2018. (KOREAN CENTRAL NEWS AGENCY/KOREA NEWS SERVICE VIA AP)

In his following visit to the Republic of Korea (ROK) on Sunday, Pompeo told President of the Republic of Korea (ROK) Moon Jae-in that the US and the DPRK sides agreed to form working-level negotiation teams to discuss the denuclearization process and schedule for the second US-DPRK summit.

Moon told Pompeo that he would make every effort to ensure the second US-DPRK summit is a success.

The first-ever DPRK-US summit was held in Singapore on June 12. Under a joint statement signed by Trump and Kim, the United States would provide a security guarantee to the DPRK in return for Pyongyang's commitment to denuclearize the Korean Peninsula.

However, US-DPRK talks have been stuck in an impasse due to their differences over the scale of denuclearization, US sanctions, and whether to issue a war-ending declaration.

During his Sept 18-20 trip to Pyongyang, Moon held talks with Kim and signed the Pyongyang Declaration, an advancement towards the Korean Peninsula's denuclearization and the ending of hostile acts near their shared border.

Pompeo said later in response that the US was ready to immediately transform its relations with the DPRK.