"Well, I am really pleased for this opportunity".
After Pyongyang, Pompeo travels to South Korea, whose dovish president Moon Jae-in has served as a go-between for the two sides. 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.
Kim Jong-un also praised his meeting with Pompeo.
"He [Pompeo] agreed with Chairman Kim to hold the second US-North Korea summit at the earliest date possible", South Korea's presidential office said in a statement, according to AFP. "And we had a very successful morning so thank you and I am looking forward to our time here at lunch as well", Pompeo replied.
The announcement Sunday came shortly after Pompeo arrived in Seoul, following his fourth visit to North Korea, where he met with Kim. 'It was another step forward.
North Korea's leader Kim also struck a positive tone during his meeting with Pompeo. 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 later tweeted: "We continue to make progress on agreements made at Singapore Summit".
But his hosts will be looking for US flexibility on North Korean demands to improve ties and even reach a formal end to the Korean War. On Wednesday, he said there was unanimous support for this at last week's UN General Assembly, even if Russian Federation and China "had some ideas about how we might begin to think about a time when it would be appropriate to reduce them".
North Korea's leader Kim Jong-un (left) walks with US Secretary of State Mike Pompeo during his trip to Pyongyang Sunday.
After their private meeting, Kim hosted Pompeo for lunch at the Paekhwawon State Guest House.
South Korea has moved forward with various joint projects, but the US has remained skeptical of North Korea's intentions, and officials have criticized what they view as a slow pace to Kim Jong Un's 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.
While the United States has expressed satisfaction with Pyongyang's self-imposed moratorium on nuclear and missile tests, it seeks a declaration of the North's nuclear assets, specialists and facilities. On Saturday, he was in Japan; on Saturday he visited both Pyongyang and Seoul; on Monday he is expected in Beijing.
North Korea's acceptance as a nuclear state could also rattle the decades-long Nuclear Non-proliferation treaty and trigger a nuclear arms race in Northeast Asia by leading many in Seoul and Tokyo to question the American guarantee to protect its allies.
North Korean Foreign Minister Ri Yong Ho told the U.N. General Assembly late 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".
Some had argued that President Donald Trump should be awarded the Prize for his role in moving the normalization between North and South Korea.