By Agence France-Presse
Tensions spiked on Friday when Tokyo recalled its ambassador over the statue which was placed outside its consulate in Busan last month, symbolising women forced to work in Japanese military brothels mostly during World War II.
Japan argues it is against a 2015 agreement between the neighbours meant to put an end to the hugely emotional and decades-long "comfort women" issue with a Japanese apology and payment of money.
"Japan has already paid one billion yen ($8.6 million) as we sincerely fulfilled our obligation. I think it's now South Korea's turn to show sincerity in an unwavering manner," Abe said in a programme aired Sunday on public broadcaster NHK.
The plight of the women has marred relations for decades but the governments of Abe and South Korean President Park Geun-Hye reached an agreement in late 2015 to finally resolve it.
Under that accord, which both countries described as "final and irreversible," Japan offered an apology and a one-billion yen payment to surviving Korean comfort women.
South Korea is expected to have a new administration following the impeachment of Park but Abe demanded the accord be honoured.
"It is a matter of national credibility to implement (the agreement) even if the government changes," he said.
Critics of the accord say the deal did not go far enough in holding Japan responsible for wartime abuses during its 1910-45 colonial rule over the Korean peninsula.
Mainstream historians say up to 200,000 women, mostly from Korea but also other parts of Asia including China, were forced to work in Japanese military brothels during World War II.
The statue in Busan was initially removed by local authorities after South Korean activists placed it in front of the Japanese consulate in the southern port city.
But after the Japanese defence minister paid homage at Yasukuni Shrine last month -- a spot where senior convicted war criminals are honoured -- Seoul allowed the activists to put the statue back up.