"I hope to meet President Park Guen-Hye for the people of both countries...And to improve and further develop our relations," Abe said at the beginning of his meeting with South Korean Foreign Minister Yun Byung-Se.
Abe is expected to attend a ceremony at the South Korean embassy in Tokyo today to mark the 50th anniversary of the normalisation of diplomatic ties in 1965, in a sign that tensions are beginning to ease, top government spokesman Yoshihide Suga said.
Yun, who was on his first official visit to Tokyo, held talks Sunday with his Japanese counterpart Fumio Kishida, when the two men agreed there would be a summit "at an appropriate time".
In their talks, Yun and Kishida "also agreed to hold foreign ministerial talks on a regular basis, and to visit each other's country," Suga said.
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Park has previously maintained there can be no meeting with Abe until Japan makes amends for its wartime system of sex slavery, which saw as many as 200,000 mostly South Korean "comfort women" forced into servitude for Japan's Imperial military.
Park said in a recent interview with the Washington Post that "there has been considerable progress on the issue of the comfort women" and the two countries were "in the final stage" of negotiations.
Japan maintains that the issue was settled in the 1965 normalisation agreement, which saw Tokyo make a total payment of USD 800 million in grants or loans to its former colony.
The Japanese government also issued a formal apology in 1993, which remains official policy.