Japan offered a "heartfelt apology" and a one-billion yen (USD 8.3 million) payment to the South Koreans, euphemistically known as "comfort women", who were forced into Japanese military brothels during World War II.
The agreement announced on Monday was hailed by Japanese Prime Minister Shinzo Abe as a "new era" for relations, which had been soured by the unresolved issue.
Taiwan's President Ma Ying-jeou urged Japan, which ruled the island from 1895-1945, to take the same measures over Taiwanese comfort women.
"We hope the Japanese government can do better and take better care of the comfort women's welfare and dignity. Our stance has not changed."
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Ma has instructed Taiwan's representative to Japan to request immediate negotiations on the issue, according to his spokesman Charles Chen.
"We hope for concrete progress for the matter in the near future... Japan understands our demands and is willing to consider," said Foreign Minister David Lin.
The issue of comfort women and a Japanese apology remains politically charged in Taiwan and sparks regular protests.
But time is running out as the number of surviving sex slaves is falling rapidly due to old age. Out of 58 known Taiwanese survivors who had come forward, 54 have died, said the Taipei Women's Rescue Foundation, which has been assisting the women.
The foundation estimates that at least 2,000 Taiwanese women could have been forced to be comfort women.
"South Korea is only the beginning and Japan should consider how to resolve the issue with the ageing comfort women in Taiwan, China, the Philippines and Indonesia, who expect an apology and compensation," said Kang Shu-hua, director of the foundation.
Up to 200,000 women, many of them Korean, are estimated to have been sexually enslaved by Japan during World War II.