MOSCOW - The leaders of Russia and Japan acknowledged Tuesday that settling a decades-long territorial dispute poses a daunting challenge but vowed to continue negotiations.

The Soviet Union took the four southernmost Kuril Islands during the final days of World War II. Japan asserts territorial rights to the islands, which it calls the Northern Territories, and the dispute has kept the countries from signing a peace treaty. Russian President Vladimir Putin said after hosting Japanese Prime Minister Shinzo Abe for several hours of talks in the Kremlin that they need to negotiate a solution to the dispute that would enjoy public support.

“Delicate work is needed to create conditions for reaching a mutually acceptable solution,” Putin said.

“A settlement that negotiators would propose must be acceptable to the people of Russia and Japan and supported by the public.”

Abe said they instructed their foreign ministers to meet again on the sidelines of a security conference in Germany next month to continue negotiations on a possible deal. “It’s not easy to solve a problem left unsolved for more than 70 years after the war ended, but we must do that,” the Japanese prime minister said. Abe has held dozens of meetings with Putin in recent years in a bid to solve the dispute, and they agreed in November to accelerate negotiations based on a 1956 Soviet proposal to return two of the islands to Japan.

Earlier this month, the Japanese leader voiced hope that this year would mark a breakthrough in talks and spoke about an imminent change of the islands’ status — remarks that irked the Kremlin. Russian Foreign Minister Sergey Lavrov warned Japan last week that it must recognize all four islands as part of Russia as a starting point for talks — a demand that didn’t bode well for Abe’s hopes for a quick deal.

On Sunday, Kremlin foreign affairs adviser Yuri Ushakov noted that recent statements from Tokyo made the talks between the two presidents even more difficult. Speaking to the Interfax news agency before the talks, Abe emphasized that the signing of a peace treaty is needed to pave the way for closer cooperation between the two nations.