Their closed-door talks were followed by a trilateral session involving Japan's Minister Taro Kono.
Earlier on Thursday, Pompeo paid a courtesy call on President Moon Jae-in.
The US diplomat briefed them "in detail" on the results of the summit meeting between President Donald Trump and the North's leader Kim Jong-un held in Singapore on Tuesday, officials said.
In a joint statement after Tuesday's summit, Kim agreed to the "complete denuclearization" of the Korean Peninsula and Trump vowed security guarantees for the communist nation on the basis of the "new relations" between the longtime adversaries.
"The U.S. alliances with these two countries are absolutely ironclad." @SecPompeo at a joint press availability following his meeting with Foreign Minister Kang Kyung-wha and Japanese Foreign Minister Taro Kono. pic.twitter.com/7P88wjxUni
Pompeo will lead Washington's follow-up negotiations with Pyongyang, but the details were not immediately known.
"I will be the person who takes the role of driving this process forward," he told reporters.
He's expected to sit down with a high-level North Korean official as early as next week.
Pompeo said the denuclearization process can make significant progress by the end of Trump's first term in early 2021.
Regarding the issue of "major disarmament", the former CIA director said: "We're hopeful that we can achieve that in the next 2 1/2 years, something like that."
He dismissed criticism about the summit accord without the term "compete, verifiable and irreversible denuclearization" (CVID).
.@SecPompeo participates in a joint press availability following his meeting with Republic of Korea Foreign Minister Kang Kyung-wha and Japanese Foreign Minister Taro Kono, in Seoul. pic.twitter.com/xN6WZP7hkX