READ MOREThe two countries plan to sign a peace treaty, formally ending the Korean War this year, the 65th anniversary of the armistice.
"There will be no more war on the Korean peninsula and thus a new era of peace has begun," the statement says.
The two leaders agreed to work for the "complete denuclearisation of the Korean peninsula".
Smiling and holding hands, the leaders met at the heavily fortified demilitarised zone between the countries on Friday, pledging to pursue peace after decades of conflict.
Mr Kim became the first North Korean leader since the 1950-53 Korean War to set foot in South Korea, stepping over a concrete curb marking the border at the truce village of Panmunjom to shake hands with his counterpart. ■