Moon noted that it will be the first time for the leaders of the to nations to hold a meeting at Panmunjom since the Korean War ended with the Armistice Agreement in 1953, reports Yonhap News Agency.
Moon was speaking at a joint press conference with Trump at Cheong Wa Dae (Presidential Palace) in Seoul, after which the US President was to head straight to the DMZ that separates the two Koreas.
Moon said he has been invited to the DMZ as well, but his "dialogue" with Kim will take place at a later time.
The focus of Sunday's DMZ event is dialogue between Pyongyang and Washington, he added.
Trump said his upcoming meeting with Kim is "just a step". He said it "might be an important step, it might not. Probably it is a step in the right direction".
He earlier said he was seeking a "handshake" session, not a summit, at the DMZ.
On the possibility of a formal third summit with Kim, he said: "Good feeling, as far as another meeting; let's see what happens," Yonhap News Agency reported.
Meanwhile, Koryo Tours, a Beijing-based tour agency specializing in North Korea tour programmes, said on its Twitter account: "The DMZ is closed to tourists visiting from the North Korean side today."
Trump arrived at the Presidential Palace after attending a "business leaders' event" on Sunday morning with the heads of some South Korean conglomerates.
During his previous visit to South Korea in November 2017, Trump pushed for a DMZ trip with Moon by chopper. But it was cancelled due to bad weather.
( With inputs from IANS )