Pompeo also said the two sides are "pretty close" to finalizing a second meeting between U.S. President Trump and the North's Supreme Leader.
The Secretary of State added that South Korea has been an integral part of negotiations aimed at denuclearising North Korea, and he passed along Mr Trump's gratitude for the country's efforts.
Before visiting Pyongyang, Pompeo held talks in Tokyo with Japan's prime minister, and pledged that the Trump administration would coordinate and unify its strategy for denuclearization with its allies.
After a previous visit to Pyongyang in July, Pompeo had said the two foes made progress on key issues - but within hours of his departure the North condemned "gangster-like" demands from the U.S., raising questions over how much the two sides really saw eye to eye.
North Korean state media KCNA said: "Kim Jong-un expressed satisfaction over the productive and wonderful talks with Mike Pompeo at which mutual stands were fully understood and opinions exchanged".
In Seoul, Pompeo said he and Kim had agreed to soon begin working-level talks on details of denuclearization and placement of global inspectors at one of North Korea's main nuclear facilities.
"The range of inspection is what matters", Shin Beom-chul, a senior fellow at the Asan Institute for Policy Studies, told ABC News in Seoul.
Pompeo and Kim also discussed "denuclearisation steps that will be taken by North Korea and the issue of attendance by the USA government", as well as "corresponding measures" to be taken by the United States, the statement said.
All six of the country's nuclear tests since 2006 were conducted at the site - the most recent in September 2017.
Tight North Korean security left US Secretary of State Mike Pompeo literally unarmed during his trip to Pyongyang.
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"For Asia, the severity of China-U.S. frictions is taking up much attention and is, to some extent, diluting attention paid to the Korean peninsula issue", it said.
"North Korea took some steps towards denuclearisation and the United States will face criticism from the worldwide community if it continues to demand complete denuclearisation without any lifting of sanctions", said Yang Moo-jin, a professor at the University of North Korean Studies in Seoul. "Some of that is actually not even going to be about the threshold question of whether we can do this, it is more of the modalities of how to do this".
Trump and Kim held an historic first summit in Singapore in June.
A report in 2014 by the United Nations Human Rights Council concluded that hundreds of South Koreans, Japanese and other foreign nationals were kidnapped by North Korea after the end of the Korean War in 1953.
Washington and Pyongyang have sparred over the exact terms of the vaguely-worded agreement in Singapore, with the U.S. pushing to maintain sanctions and pressure against the North until its "final, fully verified denuclearisation".
Pompeo told reporters in Pyongyang the two "had a great, great visit" and that Trump sent his regards.
In recent weeks, US officials have pointed to a recent meeting in Pyongyang between Kim and Moon, when North Korea committed to dismantling a missile-engine-testing site and raised the possibility of doing the same at its Yongbyon nuclear-enrichment facility.
During Mr Pompeo's last visit to Pyongyang in July, he was denounced for making "gangster-like demands".
A stalemate followed with the two countries struggling to agree over the exact terms of the vaguely worded deal secured in Singapore, with the USA calling for a "final, fully verified denuclearisation" of North Korea, while Pyongyang says more trust is needed.