The two leaders have been at the Apec meeting in South Korea
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Russian President Vladimir Putin has arrived in Japan for talks on their rapidly expanding economic ties.
He is bringing a delegation of 100 business leaders to boost trade links between the two countries, now worth around $9bn a year.
But little progress is expected in the 60-year dispute over four small islands off Japan's coast that were occupied by the Soviet Union after WWII.
The two countries have never signed a peace treaty to formally end the war.
Japan's Prime Minister Junichiro Koizumi admitted there was a "deep gulf" over the Kuril Islands, and warned an agreement was unlikely to be reached in his talks with Mr Putin.
Support pledges
But their meetings are likely to be amicable and productive if only because Japan needs new sources of energy and Russia has huge reserves of oil and gas, says the BBC's Jonathan Head in Tokyo.
Japanese companies are investing billions of dollars to help extract natural gas in nearby regions of Russia.
Japan is also competing with China for an oil pipeline from Siberia.
Tokyo has promised to support Russia's bid to join the World Trade Organisation.
For its part Moscow is making sympathetic noises about Japan's own ambitions to become a permanent member of the UN Security Council.