South Korean Foreign Minister Kang Kyung-wha said that Japan had failed to meet victims' needs.
Moon's remark came a day after the Foreign Ministry said the issue remains unresolved, but it would not seek to renegotiate the deal.
"The 2015 agreement, which did not adequately take into consideration the victims, can not be considered a genuine resolution of the Japanese wartime sex slavery issue".
They were euphemistically referred to as "comfort women".
The decision was reached after a Foreign Ministry task force spent months reviewing the negotiating process and contents of the 2015 deal, gathering survivors' viewpoints and taking into consideration Korea-Japan relations, Kang added.
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That struck a particular nerve in the chauvinistic Japanese government, which was pleased that the deal let it off admitting full government responsibility for drafting thousands of women into sexual slavery for the Imperial Army in World War II. "Japan has kept up its side of the deal".
Despite the possibility of ties between the two countries becoming strained once more, Suga said Tuesday that Tokyo is "not thinking of moving even a millimeter on the deal".
"What the victims all wish for is a genuine apology [of Japan's] own accord", Kang added.
While there are differing opinions on what to do with the funds offered by Japan, the government has said it will not use the remaining funds - about 6 billion won ($5.6 million) - and will consult with Japan to decide what should be done.
According to the government, about 40 percent of Japan's contributed money has been accepted by victims.
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The Japanese government denies it is directly responsible, insisting that "comfort women" were recruited by civilians.
South Korean President Moon Jae-in won an election past year after promises on the campaign trail to renegotiate the deal.
Japanese Foreign Minister Taro Kono said on Tuesday that Tokyo could not accept South Korea's demands for additional measures regarding a 2015 bilateral agreement on the issue of Korean women forced to work in Japanese wartime brothels. He earlier warned against any attempt to revise the deal, saying it could make their bilateral relations "unmanageable".
That created an opportunity for Moon to back out of the agreement, but at the risk of upending South Korea's relationship with Japan at a time when the countries are united in confronting North Korea over its weapons programs. "Our stance is that we will welcome the Japanese government showing sincerity on its own initiative in helping the victims regain dignity and heal their wounds", Noh Kyu-duk, foreign ministry spokesman, told a regular press briefing.
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It will also have customized features such as purpose-built locker rooms, medical and media facilities and a dedicated entrance. The NFL have confirmed ticketing information on the three NFL London 2018 games will be available on January 18.