MOSCOW (AP) — 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 receive 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.

More high-level discussions will follow when Putin visits Japan in June to attend a summit of the Group of 20 summit.

“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. The Kremlin foreign affairs adviser Yuri Ushakov also noted that recent statements from Tokyo made the talks between the two presidents even more difficult.

Japanese Foreign Ministry spokesman Takeshi Osuga declined to comment on whether the atmosphere at Tuesday’s talks was troubled by Russia’s criticisms. But he portrayed the frequency of Putin-Abe contacts as a favorable sign.

“This was the fourth summit meeting within six months,” Osuga told reporters. “This is in general something exceptional … it’s not something we see very often in diplomacy.”

Speaking after Tuesday’s negotiations, Putin reaffirmed that Russia is interested in negotiating a peace treaty, adding that the 1956 Soviet declaration prioritized signing the document.

Abe pointed at expanding economic ties and cultural contacts between the two nations, adding that Moscow and Tokyo agree on the need to further expand links.

He noted that they agreed that a charter flight to the islands will be organized in the summer to allow Japanese to visit their ancestors’ graves.

Putin argued that while trade and investment have been growing, they are still insufficient. He invited Japanese business to invest in infrastructure projects, such as beefing up cargo transfers via the Trans-Siberian Railway and shipments through Arctic sea routes.

Speaking to the Interfax news agency before the talks, Abe emphasized that he intends to maintain intensive talks with Putin in order to reach a “mutually acceptable solution.”

Putin spokesman Dmitry Peskov told reporters after the negotiations that many rounds of talks will be needed, emphasizing the need to “strengthen the atmosphere of mutual trust.”

Japanese media reports have indicated that Tokyo is open to a deal for the transfer of two smaller islands to Japan. That would mark a radical departure from the Japanese demand for the return of all four islands, but the prospect still angered Russian nationalist circles.

Several dozen demonstrators gathered outside the Japanese Embassy in Moscow to protest against the islands’ return. One of the protesters held a placard reading: “We didn’t vote for the sale of the islands.”

Left-wing activist Sergei Udaltsov said Tuesday that 11 protesters were detained by police.

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Nataliya Vasilyeva contributed to this report.