North Korea will openly close its main nuclear test site in May and its leader Kim Jong-un shared his expectations from a summit meeting with US President Donald Trump, South Korea said on Sunday.

Yoon Young-chan, senior press secretary for South Korean President Moon Jae-in, said at a press briefing that during the April 27 summit, Kim told Moon that he will shut down the nuclear test site and show the process to the world, Xinhua news agency reported.

Kim said he will invite experts and reporters of South Korea and the US to North Korea for the transparent shutdown. Pyongyang conducted all of its six nuclear tests in the Punggye-ri test site.

Moon and Kim held the third-ever inter-Korean summit in the South Korean side of the border village of Panmunjom. Kim became the first North Korean leader to step onto South Korean soil since the end of the 1950-1953 Korean War.

After the summit, they confirmed a common goal of the complete denuclearization on the Korean Peninsula, and agreed to have multilateral talks, including China and the US, to declare an end to the Korean War and alter the current armistice agreement into a peace treaty by the end of this year.

The peninsula remains technically at war as the war ended with armistice, not a peace treaty.

Kim told Moon that the Punggye-ri test site is in a good shape, rebutting the contention by some media that North Korea would close the already collapsed nuclear test site.

Moon welcomed Kim's decision to openly shut down the nuclear test site, agreeing to discuss when to invite experts and reporters of South Korea and the US to North Korea.

Kim told Moon that the US will realise, after holding talks with Pyongyang, that North Korea was not a country to use its nuclear weapons toward South Korea, the Pacific Ocean, or the US.

The North Korean leader said his country has no reason to live with difficulty because of the nuclear programme when it meets the US frequently and build mutual trust to promise the end to the Korean War and non-aggression.

The summit between Kim and US President Donald Trump is forecast to be held in May or early June.

Kim told Moon that there will be no repetition of war on the peninsula, strongly affirming that there will never be any use of force.

In a separate press briefing, Moon's spokesman Kim Eui-kyeom said the South Korean President had a telephone conversation with Trump for 75 minutes from 9.15 p.m. local time on Saturday to exchange views over the result of the inter-Korean summit.

Trump congratulated the successful inter-Korean summit, while Moon expressed gratitude for Trump's strong support that led to it.

Moon and Trump exchanged opinions on ways to successfully hold the North Korea-US summit, agreeing to continue close consultations in a bid to reach an agreement on the summit on detailed ways to realize the complete denuclearization of the Korean Peninsula.

Moon also had a phone dialogue for 45 minutes from 10 a.m. local time on Sunday with Japanese Prime Minister Shinzo Abe to explain and share the results of the inter-Korean summit.