North Korean leader Kim Jong Un and U.S. Secretary of State Mike Pompeo agreed to arrange a second summit with U.S. President Donald Trump "as soon as possible," and discussed potential U.S. inspections of North Korean nuclear sites, South Korea's presidential office said Sunday.

South Korean President Moon Jae-in held talks with Pompeo in Seoul on Sunday evening after the top U.S. diplomat met with Kim for more than three hours during a short trip to Pyongyang that was aimed at breaking a gridlock in their nuclear talks.

Pompeo told Moon that he and Kim discussed denuclearization steps to be taken by the North and the issue of U.S. government inspections of those actions, which Washington has been calling for, as well as what measures the United States will conduct in return, according to Moon's press secretary, Yoon Young-chan.