The Soviet takeover of the islands in the closing days of world war II has poisoned relations between the two countries for 70 years.
![Many people on the internet are angry at the couple [Twitter/@babyibeenajoint]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'100'%20height%3D'100'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "Many people on the internet are angry at the couple [Twitter/@babyibeenajoint]")
"We believe it is important to patiently continue the search for a solution that would satisfy the interests of Russia and Japan and that would be accepted by the nations of both countries," Putin said at a news conference following the talks.
He added that Russia would "assist" in allowing Japanese citizens to visit the Kuril islands.
"Solving (the dispute) is not easy but we would like to end it within the lifetime of our generation," Abe said.
He added that Tokyo was "thankful" to Moscow for allowing Japanese citizens to visit the graves of relatives on the islands.
Earlier, Abe said he hoped for a "new breakthrough" in settling the territorial dispute over the Kuril Islands and that he was "ready to reinforce cooperation in a calm but energetic manner."
The summit is the latest attempt to draw a line under World War II since Japan and the Soviet Union began discussions in 1956.
Abe's late father Shintaro took the lead in negotiations with Moscow as a foreign minister but died in 1991 after pushing for talks while suffering from cancer.
Japan has been careful to avoid criticising Russia, particularly its role in Syria that has drawn condemnation by Western countries, as it seeks to resolve the territorial dispute.
North Korea
The two leaders also discussed the North Korea crisis.
Putin called on countries participating in regulating the North Korea crisis to show "restraint in order not to allow a new spike in confrontation and to keep the situation in the political and diplomatic field."
"The most important (thing) is for North Korea to carry out full and irreversible denuclearisation," Abe said for his part.
Russia has retained close ties with its Soviet ally North Korea, while Pyongyang has test fired ballistic missiles over Japan.
Japan and Russia were both members of six-party talks on regulating the North Korea crisis, which also involved China, the US and both Koreas.
The talks were designed to offer the North security and economic benefits in exchange for denuclearisation but broke down in 2009 when Pyongyang abandoned them.
Putin and Abe pledged to "reinforce cooperation" at a time of tension with the West.
"I am very pleased to have the opportunity to talk in detail on our bilateral relations and political cooperation," Putin said as he greeted Abe in the Kremlin.
The two leaders already met this week on the sidelines of the Saint Petersburg Economic Forum where Abe was present as a guest of honour.
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