Moon, who played a key role in organizing historic summits between the United States and North Korea, seemed to favor talks in remarks during a videoconference summit with leaders of the European Union, Yonhap and News 1 reported Wednesday.
A senior official at Seoul's presidential Blue House told reporters Moon had said "there is a need to pursue dialogue before the U.S. presidential election" in November.
"South Korea hopes the United States pushes forward with U.S.-North Korea dialogue before the presidential election," Moon said, according to the Blue House. "South Korea is also planning to do its best so that the United States and North Korea can sit down and share in dialogue."
The statement from the Blue House comes after U.S. Deputy Secretary of State and U.S. top envoy on North Korea Stephen Biegun said it is "probably unlikely" Trump and Kim would meet before U.S. elections, during a forum of the German Marshall Fund of the United States.
Trump and Kim have not made public contact since June 2019, when the two leaders met at the truce village of Panmunjom.
North Korea has rejected paths toward denuclearization, citing international and U.S. sanctions.
Moon has said in past speeches advances in U.S.-North Korea relations are key to inter-Korea cooperation. The South Korean leader has proposed railway projects and sports exchanges with the North, but Pyongyang has instead blamed the South for the activism of defectors and demolished the Inter-Korean Liaison Office in Kaesong. More recently, Kim Jong Un called off military action plans against the South.
The Blue House did not address the North's actions on Wednesday.