"I sincerely congratulate you that the 19th National Congress of the Communist Party of China has been successfully held, and that you have been reelected the general-secretary of the Communist Party of China," Moon said in his letter to Xi.
Xi's reelection as the party chief ensures the second half of his 10-year presidency.
Moon expressed hope to hold talks with Xi in the near future to discuss various issues, including ways to establish peace on the Korean Peninsula and in their shared region.
"I hope to meet with you president in the near future and closely work together to further develop the Korea-China relationship that just celebrated the 25th anniversary into a practical strategic partnership, and to promote peace and development in the Korean Peninsula and the Northeast Asian region," he said, according to the letter released by the South Korean presidential office Cheong Wa Dae.
Seoul-Beijing ties have deteriorated over the past few months due to what many here believe to be China's economic retaliation against South Korea for the deployment of the US THAAD missile defense system here.
Moon and Xi held bilateral talks on the sidelines of the Group of 20 summit held in Hamburg, Germany in July.
They are both expected to attend the Asia-Pacific Economic Cooperation economic leaders' meeting, slated to be held in Da Nang, Vietnam in November. They are also scheduled to attend the East Asian Summit and the Association of Southeast Asian Nations meetings that will be held in Manila on Nov. 12-15. (Yonhap)