* Russian ties with Japan are improving rapidly
* Both countries wary of China’s rising influence
* Islands dispute hampering trade (Adds Putin and Abe quotes)
By Timothy Heritage and Alexei Anishchuk
SOCHI, Russia, Feb 8 (Reuters) - Russian President Vladimir Putin agreed on Saturday to visit Japan in the autumn, fuelling hopes of progress on a territorial dispute dating back to World War Two that is hampering trade.
At talks during the Winter Olympics in Sochi, Putin and Japanese Prime Minister Shinzo Abe greeted each other warmly and hailed the speed at which relations between their countries were improving - in contrast to Tokyo’s strained ties with Beijing.
Agreement is not close in the dispute over the ownership of four Pacific islands, but the two leaders have held five summits in the last 13 months and agreed in Moscow last April to revive talks on a treaty which would unblock trade and business ties.
“Since I visited Russia the pace has been very fast. We want to keep up the pace,” Abe told a news conference at which he announced Putin’s visit to Japan but set no exact date.
“Agreeing a peace treaty is the most difficult challenge, a historic mission,” he said. “We should not leave this to the next generation.”
The islands, northeast of Hokkaido, are known as the Southern Kuriles in Russia and the Northern Territories in Japan.
The Soviet Union seized them after it declared war on Japan in August 1945, forcing 17,000 Japanese to flee days before Japan surrendered.
Abe, who will also see Putin at a summit of the Group of Eight industrial powers in Sochi in June, came to the Winter Olympics in a show of support for Putin.
Several other world leaders, including U.S. President Barack Obama, did not attend the Games’ opening ceremony after international criticism of Putin’s record on gay rights.
Putin responded to Abe’s gesture by making clear he was committed to strengthening ties with Tokyo, praising an improvement in trade, although Moscow has said a major breakthrough will depend on concluding a formal peace treaty on the islands.
“We have seen a good environment created that could help resolve the most difficult problem in bilateral relations,” Putin said before talks began.
Abe’s relationship with Putin stands in marked contrast to Japan’s sharply deteriorating ties with China and South Korea, involving spats over tiny uninhabited islands, although Abe said: “The Japanese door to China is always open.”
Russia has been strengthening political and energy ties with Beijing, and President Xi Jinping also attended the start of the Games in Sochi, but Moscow is also uneasy about China’s rise and is keen to strengthen energy and trade ties in Asia.
Putin made an official visit to Japan in 2005, during his initial 2000-2008 presidency, and visited again as prime minister in 2009. Abe’s visit in April was the first official visit to Moscow by a Japanese prime minister in a decade.
Abe and Putin have not let the islands dispute block progress in diplomacy, centring on natural gas and other natural resources.
By contrast, the leaders of Chinese and Korean leaders have rebuffed Abe’s repeated calls to meet.
Some Russian oil flows are being redirected to Asia via the East Siberia-Pacific Ocean pipeline, and Russia plans to at least double oil and gas flows to Asia over the next 20 years as it turns away from export routes to Europe.
Japan sees this as an opportunity. It has been forced to import huge volumes of fossil fuel to replace its entire nuclear power industry, shut down after the 2011 earthquake and tsunami wrecked the Fukushima plant.
Japan now consumes a third of global liquefied natural gas shipments, a key reason for its record 18 months of trade deficits. Russian gas lies on Japan’s doorstep and already makes up about a tenth of its LNG imports. (Writing by Timothy Heritage; Editing by Andrew Heavens)