Pompeo and Kim also agreed to form a working group "at an early date" to discuss the denuclearization process and the second summit, which Kim proposed to Trump in a letter last month, Yoon said. -North Korea diplomatic contact since the June summit between the leaders of the two countries in Singapore.
The meeting in Pyongyang involved South Korea Unification Minster Cho Myoung-gyon and senior North Korean official Ri Son Gwon, chairman of the North Korean agency that deals with inter-Korean affairs.
Pompeo said he had a "great visit" and a "very successful morning", adding that Trump sent his regards.
Moon, who held three summits with Kim this year and also brokered the Trump-Kim summit in Singapore, said the "whole world" was watching with keen interest the outcomes of Pompeo's trip.
Instead, the top US diplomat has been tasked by his boss with preparing for a second summit with Kim Jong Un, which the North Koreans are pushing for, but that analysts warn will hurt USA goals.
Their meeting took after Pompeo returned from his trip to Pyongyang to meet with North Korean leader Kim Jong-un earlier in the day.
Mr Trump and Mr Kim held a historic summit there in June that resulted in a vague agreement for the North to denuclearise.
USA secretary of state Mike Pompeo, left, shakes hands with Japan's prime minister Shinzo Abe at Abe's office in Tokyo on Saturday. "They believe that without nuclear weapons, they are as good as dead".
Pompeo met with Japanese Prime Minister Shinzo Abe in Tokyo on Saturday, and the two men "agreed that pressure must continue until the DPRK (Democratic People's Republic of Korea) denuclearizes", State Department spokeswoman Heather Nauert said.
US SECRETARY OF STATE MIKE POMPEO, speaking to South Korean President Moon Jae-in, on his meeting in North Korea.
Pompeo departed from Tokyo, where he spent the first leg of a tour that will include stops in Pyongyang, South Korea and China.
Recently, he angered North Korea by insisting that global sanctions must remain in place until it gives up its nuclear weapons.
No sitting USA president has visited North Korea, which according to human rights groups remains one of the most repressive countries on Earth. Instead, they want both sides to take a "phased" approach, where Pyongyang is rewarded as it takes gradual steps to roll back its nuclear program.
Pompeo has repeatedly refused to discuss details of negotiations, including a US position on North Korea's demand for a declared end to the Korean War and a proposal from Seoul for such a declaration to be accompanied by a shutdown of the North's main known nuclear facility.
Kono also said he and Pompeo didn't go into details of a possible war-end declaration because it's premature while there is virtually no progress in denuclearization.
The brief trip, his fourth since March, was initially planned in late August but called off at the last minute by U.S. President Donald Trump who blamed lack of progress.
While Pyongyang has not yet signaled that it is ready to offer any such list, North Korea did, during last month's inter-Korean summit in Pyongyang, put forward a new proposal: It would dismantle its Yongbyon nuclear facility in return for "corresponding measures" from the United States.
But even on that, he said, "I doubt we'll get it nailed" down on this trip.