President Moon Jae-in and North Korean leader Kim Jong-un / Korea Times file

North Korean leader Kim Jong-un has exchanged letters with South Korea's outgoing President Moon Jae-in earlier this week in an "expression of their deep trust," state media reported Friday.

Kim received a "personal" letter from the South Korean president Wednesday, and sent a reply letter the next day, according to the North's official Korean Central News Agency (KCNA).

"Sharing the same view that the inter-Korean relations would improve and develop as desired and anticipated by the nation if the North and the South make tireless efforts with hope, the top leaders mutually extended warm greetings to the compatriots in the North and the South," it said in an English-language report.

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In his letter, Moon expressed his desire that both the South and the North make a joint declarations to establish "the foundation" for reunification even after his retirement, while Kim appreciated the "pains and effort" that Moon gave for the "great cause of the nation," according to the KCNA.

"The exchange of the personal letters between the top leaders of the North and the South is an expression of their deep trust," it added.

The exchange of letters comes as Moon's term is set to end May 9. (Yonhap)