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The conservative Japanese leader sent an official to participate in the annual demonstration in western Shimane prefecture to exert Japan's claims over small islets known as Dokdo in Korean and Takeshima in Japanese.
On a visit to Washington, Abe said that ties between the two US allies "cannot be severed" due to the exchanges between their people, their economic relationship and shared challenge of North Korea.
"I think the relationship that we have with South Korea and the cooperation that we can achieve is extremely important," Abe said at the Center for Strategic and International Studies.
"While we do have the Takeshima issue, I would like to try to work to resolve this issue and have a good relationship with South Korea."
Abe tasked Deputy Prime Minister Taro Aso to travel to Seoul to attend Monday's inauguration of president-elect Park Geun-Hye, whom Abe said he has met twice himself.
In a sign of the deep family history among Asian leaders, Abe said that his grandfather -- former prime minister Nobusuke Kishi -- was "best friends" with Park's father, late dictator Park Chung-Hee.
South Korea's foreign ministry lodged a protest after Abe's government sent Aiko Shimajiri, a parliamentary secretary in the Cabinet Office, to the rally of around 500 people in Shimane.