"South and North Korea confirmed the common goal of realising, through complete denuclearisation, a nuclear-free Korean peninsula," they said in a joint statement.
They also agreed that they would this year seek a permanent end to the Korean War, 65 years after the hostilities ended in an armistice, rather than a peace treaty.
The two Koreas will seek meetings with the United States and possibly China -- both of them parties to the ceasefire -- "with a view to declaring an end to the War and establishing a permanent and solid peace regime", the statement said.
Moon would visit Pyongyang "in the fall", the two leaders said, agreeing also to hold "regular meetings and direct telephone conversations".
There would also be a reunion of families left divided when the Korean War ended, one of the most emotive issues for the people of the two countries.
"South and North Korea agreed to proceed with reunion programmes for the separated families on the occasion of the National Liberation Day of August 15 this year," they said in a statement, referring to Japan's surrender at the end of World War II.
Around 57,000 families in the South still have members in the North.
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