Ties between the two neighbours - both of them U.S. allies threatened by nuclear-armed North Korea - remain tense over statues placed outside Japanese diplomatic missions by South Korean activists in memory of the victims.
A South Korean investigation appointed by the government concluded last month that the dispute over the women could not be " fundamentally resolved" because the victims' demand for legal compensation had not been met.
Ousted president Park Geun-Hye sought to end the decades-long row with a 2015 agreement that included a Japanese apology and payment of one billion yen ($8.8 million) to survivors.
Kang said that even though the deal was flawed, South Korea was not seeking to change it.
Foreign Minister Kang Kyung-wha told a nationally televised press conference that the 2015 agreement, which failed to reflect opinions of the victims, can not become a real resolution to the "comfort women" issue.
"Considering that, our government will not demand renegotiation of the deal", Kang told reporters Tuesday.
"We still call on Japan to accept the truth in accordance with universally accepted standards and keep making efforts to recover their dignity and heal the wounds in their minds", she added.
Kono said the 2015 settlement was a "final and irreversible resolution".
Her Japanese counterpart, Taro Kono, meanwhile described the deal as "irreversible", saying that it created a "crucial" foundation for cooperation between the two USA allies "amid efforts to address threats from North Korea".
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".
Seoul will not ask Tokyo to revise a bilateral pact on settling Japan's wartime sex slavery of Korean women.
But a refund "would amount to scrapping the agreement", a Foreign Ministry official in Tokyo said. The flames were forcing the South Korean Coast Guard's search and rescue team to stay as far as 4.8km away from the tanker, two South Korean officials said.
South Korea failed to remove a statue commemorating comfort women from in front of the Japanese Embassy in Seoul after agreeing to "solve" that issue "in an appropriate manner".
The measures were announced after a government task force, which was launched after President Moon Jae-in took office in May, concluded late past year that the previous government of ousted President Park Geun-hye failed to make sufficient efforts to listen to the surviving former comfort women.
Under the 2015 accord, Japan apologized and promised to pay $8.8 million for care for survivors.
But he has also vowed to "normalise" ties with Japan. South Korea in turn pledged to not criticize Japan over the issue.
Japan colonised the Korean peninsula between 1910 and 1945 and occupied parts of China before and after the war.