(CNN) The leaders of Russia and Japan have said they remain committed to eventually signing a peace treaty, decades after the end of World War II, but that serious differences remain over the fate of a small group of islands off the coast of Japan .

Disagreement over the sovereignty of the Kuril Islands, the southernmost of which lies just kilometers off Japan's northern island of Hokkaido, dates back to 1945 when they were occupied by the Soviet Union in the closing days of the conflict.

After the two leaders met in Moscow Monday, Russian President Vladimir Putin said the issue was front and center of their talks, but added that "painstaking work is ahead for us to create conditions for achieving mutually acceptable solutions," according to Russian state media.

He said any peace treaty "should be acceptable to the people of Russia and Japan and supported by the public at large in both countries."

Kunashiri island, part of an archipelago under Russian control, seen from the Rausu Kunashiri Observatory Deck in Rausu, Hokkaido prefecture.

'Kurils are Russian land!'

For many Russians, the idea of returning the islands to Japan is anathema. A handful of Russian nationalists took to Moscow's streets Sunday, demanding that their government stand firm and chanting "(The) Kurils are Russian land!"

Last week Sergey Lavrov, Russia's top diplomat, played down the chances of the island chain returning to Japan during a meeting with his Japanese counterpart, Taro Kono, with the Russian insisting that "sovereignty over the islands was non-negotiable ," according to Russian state media.

"This is Russia's territory," he said.

A statement posted on Japan's Ministry of Foreign Affairs website called the leaders' talks an "open frank discussion," and said Tokyo welcomed "the start of a concrete negotiation ... and (a) direct and serious discussion on the issue."

It said the two sides also agreed to widen cooperation on various issues, such as border security and economic cooperation. They also aim to increase tourism between the two nations to a total of 400,000 visitors by 2023.

Putin and Abe agreed specifically to step up economic cooperation on the disputed islands in an attempt to build trust. Japan and Russia will work together on aquaculture, greenhouse farming, wind energy, tourism and garbage processing, Russian state media outlet TASS said.

A tourist takes pictures of an islet making up part of the Habomai Islands at Cape Nosappu, a point on the Nemuro peninsula, Hokkaido prefecture.

In addition, emergency monitoring and assessment centers will be built on two of the islands, Iturup and Kunashir, TASS reports

"I believe that this visit will certainly benefit bilateral relations and take us closer to resolving the key issues of our cooperation," Putin said.

After the islands were occupied at the end of World War II, as many as 17,000 Japanese citizens were expelled. Around 19,000 settlers currently live on them, according to intelligence firm Stratfor.

They are referred to as the Southern Kurils by Russia and the Northern Territories by Japan. They consist of four islands: Iturup, known in Japanese as Etorofu, Kunashir, or Kunashiri, Shikotan and the islet group of Habomai.

According to the Japanese Ministry of Foreign Affairs' website, the islands "are an inherent part of the territory of Japan, which have never been held by foreign countries. However, the Northern Territories have been under illegal occupation by the Soviet Union, and then Russia, since the Soviet Union occupied them in 1945."

It says the Japanese government "has energetically been continuing negotiations with Russia based on its basic policy of resolving the issue of the attribution of the four Northern Islands and concluding a peace treaty with Russia."