A screen showing a picture of South Korean President Moon Jae-in and North Korean leader Kim Jong Un, is seen during a ceremony to mark the first anniversary of Panmunjom declaration which was held in Apr 27, 2018, outside of the Peace House at the southern side of Panmunjom in the Demilitarized Zone, South Korea, on Apr 27, 2019. (Photo: REUTERS)

The exchange of letters came against a backdrop of strained cross-border ties since a failed North Korea-US summit in 2019, and flaring tension after Pyongyang launched intercontinental ballistic missiles last month.

Moon sent a letter on Wednesday and promised to continue to try to lay a foundation for unification based on joint declarations reached at summits in 2018, despite the "difficult situation," KCNA said.

Kim said in his reply on Thursday that their "historic" summits gave the people "hope for the future", and the two agreed that ties would develop if both sides "make tireless efforts with hope.”

KCNA said the exchange of letters was an "expression of their deep trust."