Moon, whose next step is a third summit with Kim in Pyongyang sometime in September, called for peace, economic development and an end to weapons proliferation that escalated tensions, South Korean news service Money Today reported Wednesday.
"We must overcome such a division for our survival and development. Even though a political unification may be a long way from here, establishing peace between the South and the North and freely visiting each other, and forming a joint economic community is true liberation to us," Moon said, according to Yonhap.
Moon also said North Korea's "complete denuclearization" should be met with "corresponding measures" from the United States.
North Korea has called for an official end-of-war declaration while the United States has maintained denuclearization must come first. To settle the issue, U.S. Secretary of State Mike Pompeo could visit Pyongyang by the end of August, according to reports.
Moon is ready to provide economic incentives, should North Korea agree to a timetable for denuclearization and discloses information on its nuclear arsenal to Pompeo, according to Money Today.
Those incentives include re-connecting an inter-Korea railroad, part of an economic cooperation package Seoul is ready to deliver to Pyongyang should Kim take the first steps toward complete denuclearization.
"The development of South-North Korean relations is not an additional outcome of development in North Korea-U.S. ties. Rather, the development of South-North Korean relations is the driving force that promotes denuclearization of the Korean Peninsula," Moon said.
South Korean news service Newsis reported Wednesday Moon's package includes South Korean assistance in rebuilding North Korea's infrastructure and setting up "inland factories."
Moon's package bears similarity to Vietnam's initial measures in economic reform, according to the report.