South Korean Prime Minister Lee Nak-yon sat down with Russian President Vladimir Putin on Wednesday on the sidelines of the Fourth Eastern Economic Forum in Vladivostok, Russia.
"Let's conclude a peace treaty before the end of this year, without any pre-conditions".
Russian Federation and Japan have been in dispute for seven decades over the islands and as a result have still not formally ended their World War Two hostilities.
These were occupied by the old Soviet Union in 1945 but have always been claimed by Japan.
It has kept the two countries from signing a peace accord.
The two have met almost 30 times, and Putin said that the Chinese president is the only world leader whom he once invited to celebrate his birthday.
"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?'" Abe added.
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The South Korean PM also said that President Moon proposed to try to increase the bilateral trade volume by 50 percent by 2020, which marks the 30th year anniversary of the establishment of diplomatic relations between the two countries.
China's Global Times newspaper said China and Russian Federation could "create a vital influence" when the two countries worked together. "We are both fully aware that it will not be easy". "Putin does not expect anything", Kunadze told Echo of Moscow radio station.
In response, Russian and Japanese foreign ministry officials pointed out that work on a future agreement would continue as usual.
But a Japanese government spokesman said the country's stance had not changed.
During the Russia-Japan summit Monday, Abe called for an end to a territorial dispute over the Kuril Islands, while Putin said there is a need to "take precautions" to find a solution, according to Japanese press reports. Putin, dressed in an apron showed Xi how to pour dough on a frying pan and turn pancakes.
Sushi, of course, would be on the menu if he and Abe finally end this 70-year-old stalemate.