Against the background of growing tensions on the Korean peninsula, South Korea's outgoing President Moon Jae-in has sent a personal farewell letter to North Korea's ruler Kim Jong Un.

Moon called on Kim to seek dialogue with the new government under President-elect Yoon Suk Yeol, the Seoul Presidential Office said on Friday.

Moon also expressed his hope that Pyongyang could very soon resume talks with the United States about North Korea's nuclear weapons program, which are currently deadlocked.

Kim reportedly replied to Moon's letter on Wednesday on Thursday.

This was initially reported by the North Korean state media.

"The exchange of personal letters between the leaders of North and South Korea is an expression of their deep trust," the reports said.

Both believe that relations between the two countries can improve if they make constant efforts.

The exchange came at a time of greater uncertainty.

The USA and South Korea fear that North Korea could soon carry out a new nuclear test after repeated missile tests this year.

At the end of March, neighboring countries and the USA were particularly alarmed by the launch of a North Korean ICBM.

UN resolutions ban North Korea from testing ICBMs and other missiles capable of carrying a nuclear warhead.

Moon and Kim met three times in 2018 for lengthy talks, including twice in the border town of Panmunjom and at a summit in the North Korean capital of Pyongyang.

They had agreed to end all hostilities.

They also exchanged letters afterwards.

The left-liberal Moon, who is stepping down in May after five years in office, had pursued a course of rapprochement with the largely isolated neighboring country on the basis of the alliance with the USA.