In Washington, White House spokeswoman Sarah Sanders said in a statement that Moon briefed Trump on his plan to send a special envoy to Pyongyang on Wednesday to meet Kim.
The South Korean delegation will fly to the North Korean capital, using a direct route across the inter-Korean border.
These five officials went to Pyongyang in March to arrange the historic Panmunjom summit.
An authoritarian nation obsessed with big milestones, North Korea will use the celebration for the 70th anniversary of its national founding to glorify Kim Jong Un as a leader who's standing up for a powerful nation surrounded by enemies.
A South Korean presidential delegation has met with North Korean leader Kim Jong Un in Pyongyang and has conveyed a personal letter from South Korean President Moon Jae-in.
The five-member special delegation, led by Chung Eui-yong, top national security adviser of the Blue House, planned to visit Pyongyang Wednesday morning and return home on the same day.
Last month Trump ordered Secretary of State Mike Pompeo to abruptly cancel a planned trip to Pyongyang, citing lack of progress on denuclearisation.
The visit by the South Korean officials also comes amid an apparent impasse in the denuclearization talks between the United States and North Korea.
The current stalemate between Washington and Pyongyang has raised fundamental questions about Kim's supposed willingness to abandon his nukes, questions that were initially brushed aside amid the soaring, and so far largely empty, rhetoric surrounding a June summit between Kim and President Donald Trump that saw very little substance in its wake.
North Korea is said to have demanded a timely quid pro quo for its denuclearization efforts while the USA has repeatedly vowed to maintain maximum sanctions on the impoverished North until it completely denuclearizes.
Kim was paraphrased in the statement by his propaganda specialists as saying that it was "his will to completely remove the danger of armed conflict and horror of war from the Korean peninsula and turn it into the cradle of peace without nuclear weapons and free from nuclear threat".