Monday's high-level talks, taking place on the northern side of the truce village in the Demilitarized Zone, were proposed by the North last week as it lashed out at Washington for pushing ahead with sanctions.
Kim Eui-keum, a spokesman for Moon, said that holding the summit before September 10 would be hard due to logistics.
Mr Cho, the chief of the South Korean delegation, said the two sides also "talked a lot" about worldwide sanctions meant to punish the North for its development of nuclear weapons, but he did not elaborate.
The rival Koreas have agreed to hold a third summit between their leaders in Pyongyang sometime before the end of September.
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In a three-sentence joint statement, the two sides did not mention an exact date for the summit and provided no details on how to implement past agreements.
"The September summit can be viewed as North Korea's strategy to find a breakthrough in its stalled talks with the U.S.", said Asan Institute of Policy Studies analyst Go Myong-hyun. Former South Korean President Roh Moo-hyun also met Kim Jong Il in Pyongyang in 2007.
In the recent decade, North Korea has often repatriated South Koreans who illegally went to the country, which critics see as a message for the Seoul government to do the same for its citizens that defected to the South.
Moon and Kim met in Panmunjom on April 27 for the first time, agreeing to hold another summit in Pyongyang in fall. At the summit, North Korean leader Kim Jong-un committed to the complete denuclearization of the Korean Peninsula and US President Donald Trump promised to provide a security guarantee for the North Korean regime.
North Korea is thought to have a growing arsenal of nuclear bombs and long-range missiles and to be closing in on the ability to reliably target anywhere on the US mainland.
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There had been local media speculations that the two Koreas already agreed upon the date and venue for the third Moon-Kim summit as the two sides had working-level contacts before the high-level dialogue.
The two Koreas agreed to hold the reunion of Korean families separated across the heavily-armed border since the 1950-53 Korean War ended with an armistice.
Cho said he will listen to the North's views and firmly explain Seoul's position.
Experts say there has been slow progress on those efforts since the Singapore summit.
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