Kim expressed his will to visit President Moon Jae-in’s official home, known as the Blue House, “at anytime” if an invitation was extended, said Yoon Yong-chan, a South Korean presidential official.

Kim and Moon have been holding talks in the Peace House, just south of the border in the demilitarised zone separating the two Koreas.

Moon reacted positively to the suggestion, replying there was a better view from the Blue House, according to Yoon.

Earlier on Friday, Kim walked across the border between the two Koreas - the first time a North Korean leader had stepped foot on South Korean soil since the end of the Korean war in 1953.

The meeting was also the first inter-Korean summit in more than a decade.

Kim wrote in a guest book before the talks started, “A new history begins now – at the starting point of an era of peace.”

Moon earlier waited for Kim to arrive on the southern side of the small concrete line that represents the border dividing the two Koreas in the truce village of Panmunjom.

The leaders met near the small blue conference rooms used by the United Nations Command Military Armistice Commission, where representatives from the two sides have occasionally met in past decades.

Kim smiled as he approached Moon and the two men shook hands. Kim then stepped across the line that marks the border.

The North Korean leader received flowers handed over by two children and passed them to his sister Kim Yo-jong, who forms part of her country’s delegation.

The two leaders then attended a brief welcoming ceremony.

Both leaders were shown smiling in live television pictures as Kim signed the guest book before the talks began.

“We should achieve good results by talking frankly about current issues ... it’s a moment to write a new history of peace and prosperity,” Kim said at the start of the talks.

Moon replied: “I hope we talk frankly to reach an agreement and present a big gift for Koreans and the people around the world who wish for peace.”

The summit comes after Kim’s aggressive nuclear and missiles programme brought the peninsula to the brink of another dangerous military conflict.

Denuclearisation will be the focus of talks between the two heads of state in the Peace House, which is only a few hundred metres from the border.

Moon and Kim are expected to sign an agreement in the afternoon based on their talks.

The possibility of officially ending the Korean war, which was halted by the armistice signed in 1953, and securing permanent peace for the peninsula, may also be discussed at the summit. 

Moon has said “the signing of a peace agreement must be pursued”, as well as building a closer relationship and cooperation between the two Koreas.

If the inter-Korean summit goes well, it will also pave the way for planned talks between Kim and US President Donald Trump, to be held some time in May or June.

Ahead of the talks on Friday, a 300-soldier honour guard from the South Korean military lined up for the official welcoming ceremony in the square in front of the newly renovated Peace House.

Lines of red carpet were also laid in the area for the leaders to walk on. 

Nine senior officials from North Korea’s Workers’ Party, the military and government were due to join the ceremony.