The controversy of the so-called comfort women -- those forced into sexual slavery for Japanese troops during World War II -- has marred relations between the neighbours for decades.
Park Geun-Hye, Moon's ousted predecessor, struck a deal in 2015 with Tokyo under which Seoul promised not to raise the issue again and Japan paid 1 billion yen (USD 8.9 million) to a foundation dedicated to supporting the victims.
The agreement, in which Tokyo fell short of taking legal responsibility, angered some victims and after taking office Moon condemned the deal as a "wrongful" solution and urged Japan to make a "heartfelt apology".
"Wartime crimes against humanity cannot be covered up with a declaration that it is over.
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"The true way of resolving a tragic history is to remember that history and to learn from it," Moon said, expressing hopes for strong future relations "with the closest neighbour on the backdrop of a sincere apology".
Moon's remarks drew a swift response from Japan, which termed them "extremely regrettable".
Asked to comment on Moon's speech, top Japanese government spokesman Yoshihide Suga told a regular press conference: "President Moon mentioned the comfort women issue although we confirmed the final, irreversible conclusion in the 2015 agreement between Japan and South Korea."
Mainstream historians say up to 200,000 women, mainly from Korea but also from China, Indonesia and other Asian nations, were forced into sexual slavery for Japanese troops during the World War II.
Many South Koreans remain bitter about abuses under Japan's ruthless 1910-45 colonial rule, including the issue of the wartime sex slaves.
Most Japanese feel they have atoned enough for the country's wartime aggression, including the comfort women issue, after numerous apologies and statements on the war.
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