Democratic People's Republic of Korea (DPRK) leader Kim Jong Un described his talks with US Secretary of State Mike Pompeo on Sunday as "productive and wonderful," state media KCNA reported on Monday. 

Kim and Pompeo agreed to arrange a summit between the DPRK leader and US President Donald Trump "as soon as possible," and discussed potential US monitoring of Pyongyang's steps toward denuclearization, Seoul presidential office said on Sunday, after a closed meeting between Pompeo and President Moon Jae-in.

Pompeo also discussed additional denuclearization steps that Pyongyang can take, as well as Washington's monitoring of the verification process and "corresponding measures," the Blue House said. 

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

It added that the two sides agreed on holding working negotiations for the second DPRK-US summit as early as possible.

"The Supreme Leader expressed his will and conviction that a great progress would surely be made in solving the issues of utmost concern of the world and in attaining the goal set forth at the last talks with the projected second DPRK-US summit talks as an occasion," it added.

The KCNA said that Kim explained in detail the "proposals" intended to resolve the denuclearization issue and other matters, adding that the leader and Pompeo also exchanged "constructive" views on relevant matters. 

Besides for this, Pompeo also mentioned that international inspectors will be allowed into the DPRK's dismantled nuclear testing site.

"Chairman Kim said he's ready to allow them to come in" and see the dismantled Punggye-ri nuclear test site, Pompeo told reporters in Seoul before heading to Beijing.

The DPRK dismantled Punggye-ri in May and the dismantling was witnessed by foreign journalists who had been invited by the country's government.

The DPRK side denounced Pompeo after his last trip in July, saying he was making "gangster-like demands." Pompeo did not meet Kim during that trip. 

Kim said he believed the dialogue between the two countries would continue to develop favorably "based on the deep confidence between the two leaders of the two countries," and expressed gratitude to Trump for making a sincere effort to implement the agreement made at their historic June summit, KCNA said. 

Meanwhile, Pompeo said his latest trip to Pyongyang was "another step forward" to denuclearization and that he had a "good, productive conversation" with Kim, striking a cautious note by saying more needed to be done.

(With inputs from agencies)