TOKYO (Reuters) - As Prime Minister Shinzo Abe enters a seventh year in office, he is chasing the holy grail of Japanese diplomacy: a breakthrough in a decades-old territorial row with Russia that has stymied a formal peace treaty since the end of World War Two.

Russian President Vladimir Putin shakes hands with Japanese Prime Minister Shinzo Abe during their visit to the Mazda Sollers Manufacturing Rus joint venture plant of Sollers and Japanese Mazda in Vladivostok, Russia September 10, 2018. Valery Sharifulin/TASS Host Photo Agency/Pool via REUTERS/File Photo

Abe, who has signaled he is keen to strike a deal, is expected in Moscow next month for his 25th summit with Russian President Vladimir Putin.

Veterans of past negotiations say 2019 may be the best and last chance for Abe, who sees a treaty as a potential political legacy, to end the row over a group of windswept islands seized by Soviet troops in the final days of the war.

“Abe has only two years and nine months left in his term. If he wants to do this himself, it is a fight against time,” said Muneo Suzuki, a former negotiator and Abe confidant.

“If it goes on like this, it will end with nothing,” he told Reuters.

Putin may be open to a deal now, expecting that better ties will act as a counter-balance to China and attract more Japanese investment and technology, some experts say.

Others doubt Putin really wants any agreement, partly because a majority of the Russian public is opposed to returning any of the islands, known in Japan as the Northern Territories and in Russia as the Southern Kurils.

“I don’t believe there will be an agreement before 2021 when Abe’s stint ends,” said Valery Kistanov, head of the Center for Japanese Studies at Moscow’s Institute of Far Eastern Studies.

Hopes for an agreement have been dashed before.

A two-day summit in December 2016 ended with promises of economic cooperation but no big breakthrough on the islands.

In September, Putin caught Abe off guard when, on stage with the Japanese leader at a conference in Vladivostok, he suggested signing a peace treaty by year end “without any pre-conditions”.

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Abe later rejected the proposal, repeating Japan’s stance that the question of sovereignty must be settled first.

“TWO-PLUS-ALPHA”

After the two met again in Singapore in November, Abe told reporters they had agreed to speed up negotiations based on a 1956 joint statement in which Moscow agreed to transfer the two smaller islands to Japan after a peace treaty was concluded.

“The President and I completely share the strong determination that we will not put off this problem ... but will put an end to it with our own hands,” Abe said.

Retired diplomat Kazuhiko Togo said the remarks showed Abe was determined to clinch a deal.

“If you read Abe’s statement after the Singapore meeting ... Abe was saying very clearly, ‘I am going to do it’,” Togo said.

Suzuki said a likely deal was one in which Russia gives up the two smaller islands and retains the two larger ones, but allows Japan some access -- a formula known as “two-plus-alpha”.

A peace treaty could be signed in June when Putin is likely to visit Japan for a Group of 20 meeting, but negotiating the handover of the smaller isles would take more time, he said.

Japan has claimed sovereignty over all four islands, so a “two-plus-alpha” deal would likely be unpopular with conservative voters who make up Abe’s core political base.

In a sign of its sensitivity, Foreign Minister Taro Kono ignored questions about the islands at a recent news briefing. He later apologized, saying he should have replied “No comment”.

Moscow’s conditions for a deal could be too much for Abe to swallow. Among them is a guarantee that Tokyo will not allow U.S. military deployments on any returned islands.

Russia, which has strengthened its military presence on the larger islands, said on Monday it had built new barracks for troops and planned more facilities for armored vehicles, prompting a protest from Japan.

Hours later, though, ministers from the two countries met in Tokyo to discuss economic cooperation.

Any transfer of sovereignty to Japan would have to address the role of the U.S.-Japan Security Treaty and Washington’s right to establish military bases on the islands.

“Abe seems to want to get away with a verbal statement that no U.S. facilities would be allowed,” said James Brown, a professor at Temple University’s Japan campus. “That’s not good enough for the Russian side.”

Efforts to break the deadlock have floundered before, but failure now would be significant for Abe, said Togo.

“This is the last opportunity,” he said. “Abe has insisted for five or six years that this is his priority issue. If there is a setback, it will be weightier than in the past.”