Both men spoke through translators.
Mike Pompeo is believed to have met with Kim during this trip. On that occasion, he did not meet Kim.
Trump should declare that Washington won't sign a peace treaty with a nuclear-armed North Korea and won't support an end of Korean War declaration until Pyongyang takes significant disarmament steps, according to Evans Revere, a former State Department Asia specialist.
South Korea may find it politically impossible to accept North Korea as a nuclear state after decades of animosity and occasional bloodshed, said Cheon Seong-whun, a presidential secretary during Seoul's previous conservative government.
He arrived in Seoul, South Korea, in the evening and was scheduled to meet South Korean President Moon Jae-in. He said in Seoul that he had "a good, productive conversation" with Kim.
"As President Trump said, there are many steps along the way and we took one of them today", Pompeo told Moon. "It was another step forward", Pompeo said in a meeting with Moon at the Blue House. "So this is, I think, a good outcome for all".
A second Kim-Trump meeting looks increasingly essential, given the lack of progress their subordinates have made since the landmark first-ever North Korea-US summit in Singapore on June 12.
Pompeo said Wednesday that he's optimistic he'll come away with a plan for a second summit between Trump and Kim and progress on a "pathway for denuclearization".
The South Koreans took part earlier Friday in a joint celebration marking the anniversary of the 2007 summit, where the participants issued a statement that included a vague call for a denuclearized Korean Peninsula and urged more cross-border exchanges and cooperation between the rivals.
With talks largely deadlocked, at the heart of this round of negotiations is a debate over what the US should demand from North Korea and what it is willing to give in exchange.
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After Seoul, Pompeo ends his trip Monday in China, North Korea's political and economic lifeline.
"Today is a very important day for the U.S.as well as South and North Korea", Moon said.
The last trip to North Korea for the secretary of state, in July, did not go so well. 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 worldwide inspectors present to verify, and could be reversed.
Mr Pompeo had flown to Pyongyang from Tokyo after talks with Japan's prime minister Shinzo Abe during which he pledged the Trump administration would coordinate and unify its strategy for denuclearisation with allies.
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.
The Koreas in past months have held a flurry of talks, including three summits, amid a global diplomatic push to resolve the nuclear standoff with North Korea.
In the past few days, North Korea has also renewed its demands for sanctions to be eased.
He then held a working dinner meeting with Foreign Minister Kang Kyung-wha.