Secretary of State Mike Pompeo was ensconced in an elegant Pyongyang guest house for a second day of talks with North Korean leader Kim Jong Un's right-hand man Kim Yong Chol.

It was not clear if Pompeo would be granted an audience with the Northern leader himself as he tries to develop a detailed road map towards the "complete denuclearisation" of the Korean peninsula, as agreed by Kim and US President Donald Trump last month.

But talks continued at a large guest villa in an official compound in Pyongyang, a short distance from the imposing mausoleum where North Korea's former helmsmen, Kim's grandfather and father, Kim Il Sung and Kim Jong Il lie in state.

As the day began, Pompeo left the compound to go to a location where he could make a secure call to Trump away from potential surveillance, then returned to restart talks at around 9:00am (0000 GMT).

Kim Yong Chol asked Pompeo if he has slept well on his first overnight stay in the country. Pompeo confirmed that he had, and the pair had a brief exchange before reporters were asked the leave the room.

"We consider this very important too since it is the first senior-level face-to-face meeting since the summit between our two leaders. President Trump is committed to a brighter future for North Korea," Pompeo said.

"So the work that we do the path toward complete denuclearisation building a relationship between our two countries is vital for a brighter North Korea and the success that our two presidents demand of us."

Kim replied: "Of course it is important. There are things that I have to clarify."

"There are things that I have to clarify as well," Pompeo responded.

Pompeo, who is on his third visit to Pyongyang, began his diplomatic outreach to North Korea when he was still Trump's CIA director and remained the pointman on negotiations after the process became public and he became secretary of state."

In comparison to past international nuclear disarmament negotiations, and indeed to most major power diplomacy, the discussions between Washington and North Korea on thawing ties and dismantling the North's arsenal appear to be proceeding in reverse.

Last month, Kim and Trump met in Singapore and signed an historic joint statement committing Pyongyang to "work towards complete denuclearisation of the Korean Peninsula" in exchange for US "security guarantees" and a lasting peace in the decades-old stand-off.

- Crisis over? -

But rather than the two leaders crowning years of detailed negotiation with their one-on-one meeting, the short statement marked instead the start of a diplomatic long slog and Trump earned the scorn of Korea watchers and non-proliferation experts when he declared the crisis over.

The task of establishing the disarmament programme now falls to Pompeo, who is seeking a formal declaration by the North of the size of its nuclear programme as well as an eventual timetable for it to be stood down under international verification and inspection.

Many experts doubt Kim's sincerity -- a nuclear deterrent to the US military forces massed in South Korea has long been a strategic goal of his isolated, autocratic regime -- and few expect this to be a quick process, even if Washington wants results within a year.

Pompeo, accompanied by senior State Department and CIA officials, held several hours of talks on Friday evening and had a working dinner with Kim Yong Chol at which both were "cracking jokes" and "exchanging pleasantries," according to US spokeswoman Heather Nauert.

They also, she said, agreed to set up working parties to pursue the "nitty gritty details" of how to make good on promises made in Singapore.

They were expected to talk all day Saturday before Pompeo heads to Tokyo to brief Washington's Japanese and South Korean allies.