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.
Moon criticized the deal as gravely flawed, saying it can not resolve the comfort women issue.
But Seoul will not use any more of Tokyo's money for the survivors, replacing the funds from its own budget, Kang said, urging Tokyo to offer a "voluntary and honest apology".
The Japanese foreign minister said Japan would like further clarification as to what Seoul means by "matching Japan's contribution" and how it plans to use the funds.
But the government's decision, which appears to have been made mindful of the impact that withdrawal from the accord could have on Korea-Japan relations as well as its diplomatic credibility, drew protests from both Japan and victims of Japan's sexual enslavement.
South Korean President Moon Jae In said Wednesday that Japan needs to apologize to "comfort women" forced to work in Japanese wartime military brothels, one day after Seoul unveiled its new position on a bilateral deal on the issue.
It lets Japan off admitting direct responsibility for drafting thousands of Asian women, mostly Korean, into sexual slavery for the Imperial Army in World War II.
How the 1 billion yen raised by the Korean government to match the Japanese fund will be used is yet to be decided and will include consultations with the survivors and the Japanese government, according to a Korean Foreign Ministry official. In the meantime, the ministry will set aside the same approximately 10.8 billion won in the government budget to implement follow-up measures.
"The government focuses on a "victim-focused" approach, but why do they just move on like this?"
Mr Moon's remarks drew an angry response from Japan, with Chief Cabinet Secretary Yoshihide Suga saying that Japan "can never accept it" if South Korea were to demand more measures on top of the agreement. "But its effort to satisfy every stakeholder led to failing to satisfy any stakeholder". The Japanese government continues to take a stern stance that there could be no concession to Seoul on such a demand.
While saying it is "undeniable" that the 2015 deal is an official agreement between the two countries, the president said Wednesday the "erroneous knot" with Japan over the comfort women issue must be untied.
Moon's displeasure with the agreement has angered Japan.
South Korean news agency Yonhap reported Lu also said Japan should address other issues of history.