According to presidential spokesman Kim Eui-kyeom, Moon will hand over the invitation from Kim to the pope during his upcoming visit to Europe.
"Chairman Kim said he will 'ardently welcome the pope if he visits Pyongyang'," the spokesman said at a briefing as quoted by the Yonhap News Agency.
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The spokesman added that Moon was expected to visit the Vatican on October 17-18.
In 2000, North Korea already invited Pope John Paul II to visit the country, however, the visit never took place.
North Korea is officially an atheist country that rigidly controls religious activities.