North Korean leader Kim Jong Un yesterday said his "historic" summit with US President Donald Trump in Singapore stabilised regional security, and that he expected further progress at an inter-Korean summit aimed at reviving stalled nuclear diplomacy.

Kim thanked South Korea's President Moon Jae-in for bringing about the Singapore meeting in June as the two leaders began their third round of talks in Pyongyang.

"Thanks to that, the political situation in the region has stabilised and I expect more advanced results," Kim told Moon, referring to the Singapore gathering, at the start of their talks.

The Kim-Moon summit will be a litmus test for another meeting Kim has recently proposed to Trump, with the South Korean president seeking to engineer a proposal that combines a framework for the North's denuclearisation and a joint declaration ending the 1950-53 Korean War.

Moon expressed gratitude for Kim's "bold decision to open a new era".

The first session of the talks, which lasted for two hours, were held at the headquarters of the North's ruling Workers' Party Central Committee, with party vice chairman Kim Yong Chol and Kim Jong Un's sister Kim Yo Jong, as well as South Korea's national security adviser Chung Eui-yong and spy chief Suh Hoon in attendance.

Earlier, the leaders paraded down the streets of Pyongyang in Kim's black Mercedes limousine to loud cheers from nearly 100,000 North Koreans who waved flowers and chanted "Motherland! Unification!"

Kim greeted Moon with hugs and handshakes as the South Korean leader landed in the North's capital with a mission to rekindle momentum in faltering talks between Washington and Pyongyang over denuclearisation and a formal end to the 1950-53 Korean War.

As Kim escorted Moon to the Paekhwawon State Guest House, where Moon will stay during his three-day visit, Kim said he wanted to produce a "bigger outcome at a faster pace" than the two leaders have achieved so far.

Moon, himself the offspring of a family displaced by the war, has met Kim twice this year at the border village of Panmunjom.

Trump has asked Moon to be "chief negotiator" between himself and Kim, according to Moon's aides, after Trump cancelled a trip to Pyongyang by his secretary of state last month.

South Korean President Moon Jae-in is greeted by North Korean leader Kim Jong Un during an official welcome ceremony at Pyongyang Sunan International Airport, in Pyongyang, North Korea, September 18, 2018. Photo: Reuters

Washington wants to see concrete action toward denuclearisation by North Korea before agreeing to a key goal of Pyongyang - declaring an end to the 1950-53 Korean War.

The conflict ended with an armistice, not a peace treaty, leaving US-led UN forces including South Korea technically still at war with the North.

South Korea is pinning high hopes on Kim's remarks to Moon's special envoys earlier this month that he wants to achieve denuclearisation within Trump's first term in office ending in early 2021.

"If North Korea-US dialogue is restarted after this visit, it would have much significance in itself," Moon said before his departure.

Underscoring the challenges ahead, North Korea's official Rodong Sinmun yesterday said "the responsibility falls squarely on the United States" for the stalled nuclear discussions.

Today, Moon and Kim plan to hold a second day of official talks after which they are expected to unveil a joint statement, and a separate military pact designed to defuse tensions and prevent armed clashes. Moon will return home early Thursday.