Japan is cautiously optimistic that Soviet Foreign Minister Eduard Shevardnadze's visit beginning Sunday may ease 15 years of tense relations that have kept the economic and superpower giants from sharing in the recent East-West political thaw.

Shevardnadze, who left Moscow Saturday, arrives in Tokyo Sunday for his first visit to Japan in nearly three years with speculation running high that the Soviet Union's new-found "glasnost," or openness, may produce a Kremlin initiative on solving a 43-year-old territorial dispute between the estranged neighbors.The conflict involves a group of four islands off the coast of Japan's northernmost island of Hokkaido, which the Soviet Union claimed immediately after World War II.

Although the two countries established formal diplomatic ties in 1956, the Japanese government has said it will not sign a peace treaty with Moscow or further its diplomatic relationship until the Soviet Union returns the islands.

In 1973, Japanese Prime Minister Kakuei Tanaka and Soviet leader Leonid Breshnev agreed in Moscow that the islands remain an unsettled issue from the war, and the Kremlin has refused to discuss the issue since.

Signaling a softening of attitude, Shevardnadze this month told Japanese Ambassador to Moscow, Toshiaki Muto, that the Soviet Union was ready to talk about the so-called Northern Territories dispute during his talks in Tokyo.

"We welcome that attitude," said an official of the Japanese foreign ministry who asked not to be identified. "We hope that the positions of the two sides will become nearer. We hope their position will be more forthcoming toward us. Our basic position is unchanged, but we hope to talk very seriously."

Shevardnadze will meet three times with Japanese Foreign Minister Sosuke Uno beginning Monday, and also will talk with Prime Minister Noboru Takeshita and former Prime Minister Yasuhiro Nakasone.

Following his four days in Japan, Shevardnadze is scheduled to leave Wednesday for the Philippines.