Kim Jong Un has agreed to hold a second summit with US President Donald Trump as soon as possible, Seoul said Sunday, after Washington's top diplomat held “productive” talks on denuclearisation with the North Korean leader in Pyongyang.

US Secretary of State Mike Pompeo met with Kim on Sunday morning for around two hours of talks followed by a lunch in the North's capital, before flying to Seoul on a whirlwind diplomatic visit to the region.

Pompeo said “he 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, although no specific time or location has yet been agreed.

Pompeo and Kim also discussed “denuclearisation steps that will be taken by North Korea and the issue of attendance by the US government,” as well as “corresponding measures” to be taken by the US, the statement said.

The visit was Pompeo's fourth to North Korea.

US President Donald Trump met Kim in Singapore in June for the first-ever summit between the countries, resulting in what critics say was only a vague commitment by Kim towards denuclearisation of the Korean peninsula.

“We continue to make progress on agreements made at Singapore Summit.

Thanks for hosting me and my team,” Pompeo tweeted.

Kim also praised their “nice meeting”, telling Pompeo via an interpreter following the morning's talks that it was “a very nice day that promises a good future ... for both countries.”