It would be the first summit in more than a decade between Korean leaders.

Mr Moon said the Koreas should "make it happen" and encouraged the north to return to negotiations with the US.

The handwritten invitation was delivered by Mr Kim's influential sister, Kim Yo-jong, at a landmark meeting in the presidential palace in Seoul, as the Winter Olympics opened.

Ms Kim and the North's ceremonial head of state Kim Yong-nam made up the most senior delegation from the North to visit the South since the Korean War in the 1950s.

The figures from the two Koreas shared kimchi (Korean pickled cabbage) and soju rice liquor, and spoke for three hours.

Ms Kim invited Mr Moon to visit "at the earliest date possible", a spokesman for South Korea's presidential palace said.

According to a tweet by the Washington Post's Tokyo bureau chief, Ms Kim left a note at the palace expressing hope that "Pyongyang and Seoul will become closer in the heart of Koreans" and for "unification and prosperity in the near future".