Earlier, media reported that the envoy from Seoul met in Pyongyang with North Korean leader Kim Jong-un and handed him the message from president Moon.
Moon and Kim held two bilateral meetings earlier this year, in April and in May.
Previous month, officials from the North and South Korea began their talks on preparations for the planned high-level bilateral summit on the northern side of the truce village of Panmunjom, media reported.
Moon Jae-in and Kim Jong-un held two bilateral meetings earlier this year amid burgeoning diplomacy on the Korean Peninsula.
During their historic summit in Panmunjom in late April, the South Korean President promised to visit Pyongyang for a meeting in fall.