The two leaders met on Wednesday at the Eastern Economic Forum taking place in Vladivostok in Russia's Far East.
Should the dispute finally be put to an end, Russian Federation and Japan could formally sign a peace agreement - 71 years after the end of the World War II.
Russian President Vladimir Putin, sitting on a stage alongside Japanese Prime Minister Shinzo Abe, proposed on Wednesday (Sept 12) that the two men sign a peace treaty by the end of this year. "We have been negotiating for 70 years", Mr Putin said.
The Japanese leader, who is widely expected to win another three-year term as head of the ruling Liberal Democratic Party in a leadership vote on September 20, noted a resolution would "not be easy" but suggested he and Putin were the ones to achieve it: "Let us walk together mindful of the questions 'If we don't do it now, then when?' And 'if we don't do it, then who will?'"
Establishing its sovereignty over the islands is the crucial issue for Japan, so it would be unlikely to sign a deal without first receiving some assurances from the Kremlin over the fate of the islands.
He has reportedly met Putin 22 times, with whom he has struck up a relationship as he seeks to resolve long-term territorial and historical disputes with Russian Federation.
Mr Putin said security in the region was a key issue and that Russian Federation was concerned by a move to establish a United States missile defence system there.
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It has kept the two countries from signing a peace accord that would formally end their wartime hostilities.
"An idea has just come into my mind", Putin said at a regional economic forum in Vladivostok, which was also attended by Abe.
"This is called trolling".
Russian and Japanese Foreign Ministry officials said that work on a future agreement would continue as usual, and a Japanese official made clear that Tokyo wants an agreement on possession of the islands before it will sign a peace treaty. "Putin does not expect anything", Georgy Kunadze, a former Russian deputy foreign minister, told AFP news agency, adding that Abe would never accept a deal that would be political suicide for him.
Experts have to "conduct a thorough study of the possible economic output" of the project, Abe said.
Lying near the Japanese island of Hokkaido, the territory was taken over by Red Army troops in the final days of World War II.
Putin's predecessor, Dmitry Medvedev travelled to Kunashir in 2010, becoming the first Russian leader to visit the disputed islands and provoking fury in Tokyo.