(CNN)On Tuesday, the leaders of Japan and Russia will hold talks on what remains one of the world's longest-running unresolved international disputes.
The Kuril Islands, referred to as the Southern Kurils by Russia and the Northern Territories by Japan, were captured by Soviet forces following Japan's surrender to Allied Forces in 1945.
The resulting disagreement over who has rightful ownership of the islands has soured relations between the two countries, contributing to their continued failure to sign a World War II peace treaty.
The disputed territory, located off the coast of the Japanese island of Hokkaido, consists of four separate islands: Iturup, known in Japanese as Etorofu, Kunashir, or Kunashiri, Shikotan and the islet group of Habomai.
The two governments are pushing for a treaty to be signed based on a 1956 declaration, which acknowledged the cessation of WWII hostilities but did not set out terms for a formal peace agreement.
Japanese media states that the terms of the 1956 accord would hand over Shikotan and the Habomai islands to Japan, a sensitive notion inside Russia, where the ceding of any territory to Japan would likely be met by protests.
'This is Russia's territory'
The territorial dispute was raised ahead of Prime Minister Shinzo Abe's trip to Moscow this week to meet with Russian leader Vladimir Putin.
However, Sergey Lavrov, Russia's top diplomat, has dow