The agreement was struck as the two sides continued negotiations on the second day of talks aimed at resolving the issue, Kyodo News agency said.
The talks on the islands, called Takeshima in Japanese and Dokdo in Korean, are the neighbors' first on the topic in six years, and tough negotiations were expected because both sides want the islands as a basis to claim exclusive rights over marine resources.
A senior Japanese official stressed the importance of resolving the problem through talks, the AP reports.
Abe, speaking shortly after the talks resumed Tuesday, refused to comment on what specifically was being discussed.
The islands lie roughly halfway between the two countries and are currently controlled by South Korea, although they also are claimed by Japan. They are surrounded by rich fishing grounds and possible deposits of methane hydrate used to produce natural gas.
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