The top US diplomat met with Kim for around two hours tgus morning in the North's capital, where denuclearisation and a second US-North Korean summit were expected to be high on the agenda, before the pair shared a lunch together.
The sides particularly "discussed the upcoming second summit between President [Donald] Trump and Chairman Kim [Jong-un] and refined options for the location and date of that next summit", the statement added. Aside from Pompeo, the US side included Stephen Biegun, the new USA special envoy for North Korea, and Andrew Kim, who heads a Korea working group at the CIA that Pompeo set up while he was running the agency.
"Yeah, so we had a great, great visit this morning", Pompeo replied. "It was another step forward".
Pompeo said he and Kim had gotten "pretty close" to fixing the logistics for the summit but stressed that "sometimes that last inch is hard to close".
North and South Korea leaders met last month to rekindle the peace process.
Before traveling to Pyongyang, Pompeo met in Tokyo on Saturday with Japanese Prime Minister Shinzo Abe and Foreign Minister Taro Kono.More news: Brett Kavanaugh protests: Over 100 arrested on Capitol Hill, police say
But several experts told ABC News that North Korea hadn't done enough yet to earn an end-of-war declaration, let alone a second Trump-Kim summit.
"Then we are also going to set up the next summit", said Pompeo.
Trump canceled Pompeo's planned trip to Pyongyang in August, citing little evidence that North Korea had followed through on any of its commitments to denuclearize.
Pompeo said on Sunday his latest, fourth 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.
The top U.S. diplomat added that there was also discussion between him and Kim about "corresponding measures" to be taken by the United States as a reward for North Korea's denuclearization measures.
Pompeo has repeatedly refused to discuss details of negotiations, including a United States 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.More news: India deports 7 Rohingya as SC refuses to intervene
"The mission is to make sure that we understand what each side is truly trying to achieve", Pompeo said Friday en route to Japan, his first stop on his swing through East Asia.
"It's a very nice day that promises a good future for both countries", Kim said through an interpreter at the dining table.
In their meeting, Abe and Pompeo agreed to urge North Korea to take concrete steps toward denuclearization and to coordinate their policies aimed at compelling that outcome.
The secretary of state's last trip to North Korea, in July, did not go so well. He also pledged that during his meeting with Kim on Sunday, he would raise the cases of Japanese citizens abducted by North Korea. -North Korea summit would take place in the near future, and mark irreversible progress in achieving denuclearization and bringing stable peace to the Korean Peninsula. The steps they've taken so far - beginning to dismantle a key missile engine test site and blowing up the tunnels to a nuclear site - have been without global inspectors present to verify, and could be reversed.
North Korean Foreign Minister Ri Yong-ho told the United Nations General Assembly at the end of last month that "coercive" sanctions were lethal to trust-building between the two nations, and that without trust "there is no way we will unilaterally disarm ourselves first".
Nauert's statement made no mention of North Korea's commitment to dismantle the important Yongbyon nuclear facility, a potentially troubling sign for US negotiators.More news: Amazon ‘Fire TV Stick 4K’ and ‘Alexa Voice Remote’ in India
Trump is pressing to meet with Kim for a second time after their June summit in Singapore produced a vague agreement on denuclearization with few, if any, specifics.