Seoul controls the islands in the Sea of Japan (East Sea) which it calls Dokdo. They are known in Japan as Takeshima.
The Shimane prefectural government in southwest Japan held its annual convention Sunday, after enacting a local ordinance in 2005 which designated February 22 as "Takeshima Day".
Yohei Matsumoto, parliamentary vice minister in the Cabinet Office, attended Sunday's ceremony and said the government was working to achieve a peaceful resolution of the problem.
But he reiterated Tokyo's position that the islets are part of Japan's sovereign territory, according to local media.
The row over the islands intensified after then-South Korean President Lee Myung-Bak made a surprise visit to them in 2012.
Relations between the two countries are currently at their lowest ebb for years due to the territorial row, and disputes linked to Japan's harsh 1910-45 rule over the Korean peninsula.