Amid rising tensions on the peninsula following Pyongyang's repeated nuclear weapons tests, Moon also proposed that the two sides suspend hostile acts along their border.
In his Berlin speech, Moon also proposed holding Red Cross talks with the DPRK for the reunion of separate families of the two Koreas on October 4 that marks the 10th anniversary of the October 4 joint declaration and also the traditional Chuseok holiday.
The South's Defense Ministry on Monday proposed the meeting to be held on Friday at the border truce village of Panmunjom, which also hosted the last such negotiations in December 2015.
"Today's proposal was a step to ease tension and establish peace in the initial phase (of the new administration) while resolving the pressing matters like the separated families", Unification Minister Cho Myoung-gyon said at a separate news conference. The reunions are widely seen as a barometer of inter-Korean relations. North Korea has yet to respond to the latest overture.
Officials hope North Korea accepts their request.
South Korea's Defense Ministry made the offer on Monday morning, the first since Moon Jae-in became the South's president.
This is Seoul's first proposal for government-level talks with Pyongyang since President Moon Jae-in came to power in May.
But the unification minister said the conditions for inter-Korean talks between the South and North Korean governments led by the South Korean Ministry of Unification (MOU) "haven't been satisfied".
The stakes have risen for Trump after North Korea's first successful test on July 4 of a missile that could reach Alaska, if not continental America. Pyongyang cut off direct communications with the South in February 2016, leaving Seoul no other choice but to convey their message openly through the media, government sources said.
But Pyongyang has staged a series of missile launches in violation of United Nations resolutions - most recently on July 4 when it test-fired its first ICBM, a move which triggered global alarm and a push by US President Donald Trump to impose harsher United Nations sanctions.
Seoul's Unification Ministry says these latest proposals are in line with President Moon Jae-in's dual track policy to pursue both engagement with the Kim Jong Un government while also supporting USA led sanctions to pressure Pyongyang to halt its nuclear and ballistic missiles programs.
While Cho says there is no "separation" between the USA and South Korea on dealing with the North Korean nuclear threat, Washington continues to emphasize pressure over dialogue and is preparing new sanctions on Chinese banks and firms doing business with Pyongyang possibly within weeks, according to US officials. The two declarations aim to foster cross-border cooperation, exchanges and reconciliation. About 28,500 American troops are stationed in South Korea.