SEOUL • North Korean leader Kim Jong Un and United States Secretary of State Mike Pompeo agreed to arrange a second summit "as soon as possible", and discussed potential US inspections of North Korean nuclear sites, South Korea's presidential office said yesterday.

South Korea's President Moon Jae-in held talks with Mr Pompeo in Seoul after the top US diplomat met Mr Kim for more than three hours during a short trip earlier yesterday to Pyongyang that was aimed at breaking a gridlock in their nuclear talks.

Mr Pompeo told Mr Moon that he and Mr Kim discussed denuclearisation steps to be taken by the North and the issue of US government inspection of those actions, which Washington has been calling for, as well as the measures the US would conduct in return, according to Mr Moon's press secretary Yoon Young-chan.

Mr Pompeo and Mr Kim also agreed to form a working group "at an early date" to discuss the denuclearisation process and the second summit, which Mr Kim proposed to US President Donald Trump in a letter last month, Mr Yoon said.

"Secretary Pompeo said he and Chairman Kim concurred that they will hold the second US-North Korea summit as soon as possible," Mr Yoon said in a statement.

"The two sides also agreed to continue discussions to decide on the detailed timing and location of the second summit."

While Seoul sounded upbeat, Mr Pompeo struck a more cautious tone. He said his latest, fourth trip to the North, was "another step forward" to denuclearisation and he had a "good, productive conversation" with Mr Kim, but more needed to be done.

"As President Trump said, there are many steps along the way and we took one of them today," Mr Pompeo told Mr Moon. "It was another step forward. So this is, I think, a good outcome for all of us."

Mr Pompeo tweeted that he had a good trip to Pyongyang and that both sides continued to make progress on agreements made at the first Trump-Kim summit held in Singapore in June.

Mr Moon had his own third summit with Mr Kim last month in Pyongyang. It was partly intended to help salvage the stumbling negotiations between Pyongyang and Washington, after Mr Trump called off Mr Pompeo's planned visit to the North in late August, citing lack of progress.

Mr Kim pledged to work towards denuclearisation at the Singapore summit in June, but Pyongyang's actions have since fallen short of Washington's demands for irreversible steps to give up its arsenal, including the declaring of all nuclear and missile facilities.

At last month's meeting with Mr Moon, Mr Kim promised to allow outside inspections of key missile facilities, and expressed a willingness, for the first time, to "permanently" scrap Yongbyon, North Korea's main nuclear complex.

Departing from Tokyo, Mr Pompeo arrived in the North Korean capital before noon yesterday. He and Mr Kim met for about two hours, and then had lunch together for another hour and a half, according to a report.

"It's a very nice day that promises a good future for both countries," Mr Kim said, speaking through an interpreter.

A US official who was part of Mr Pompeo's delegation said that the trip was "better than the last time" but added: "It's going to be a long haul."

Mr Pompeo's last trip did not go well. He left Pyongyang in July hailing progress, only for North Korea to denounce him for making "gangster-like demands". Mr Pompeo did not meet Mr Kim on that trip.

Mr Pompeo is due to travel to Beijing before returning home today.