Factbox: Ties and tensions between China and Japan

(Reuters) - Japan and China have agreed to improve ties, Japan's foreign minister said on Friday after talks with his Chinese counterpart likely to set the stage for fence-mending between the leaders of Asia's biggest economies.

Japanese Foreign Minister Seiji Maehara told reporters after meeting China's Foreign Minister Yang Jiechi that the leaders of both nations, whose ties have been strained by a dispute over islands in the East China Sea, were likely to hold one-on-one talks on the sidelines of an Asian summit in Hanoi.

Here are some facts about ties between the two countries.

ECONOMIC POWERHOUSES, SHIFTING RANKINGS, RARE EARTH

* Preliminary statistics indicate China has edged past Japan to become the world's second-biggest economy, with the United States remaining the world's biggest by far.

Japan's second-quarter unadjusted gross domestic product (GDP) totaled $1.2883 trillion on a nominal dollar basis, against China's second-quarter unadjusted GDP of $1.3369 trillion. Japan and China together account for about 17 percent of the world's output.

* China-Japan trade rebounded in the first half of 2010 after slumping in the global financial crisis. Bilateral trade reached 12.6 trillion yen ($155.5 billion) in value in the first half, a jump of 34.5 percent over the same period last year, according to Japanese statistics.

Two-way trade totaled 21.7 trillion yen in 2009. China has been Japan's biggest trading partner since 2009.

* China and Japan are the world's first and second-biggest holders of foreign reserves.

* A series of strikes in China has hit Japanese firms this year, including suppliers to Toyota Motor Corp and Honda Motor Corp.

* China, which produces 97 percent of the world's rare earth metals, set its 2010 export quotas 40 percent lower than 2009 levels. Japan is worried that China has started holding back shipments of rare earths after a recent maritime dispute, while China denies cutting shipments to Japan for political reasons.

HISTORICAL TENSION

* Japan invaded and occupied part of China from 1931 to 1945. Bitterness over Japan's wartime atrocities has faded as a diplomatic flashpoint, but still underpins widespread Chinese public distrust of Japan.

* China has criticized high-profile visits by Japanese politicians to Tokyo's Yasukuni Shrine for the war dead. Among those honored at the shrine are 14 Class A war criminals convicted by an Allied tribunal after World War Two.

Junichiro Koizumi, Japanese prime minister from 2001 to 2006, made annual visits to the shrine while in office but his successors have stayed away.

TERRITORIAL DISPUTES AND MILITARY TENSION

* Japan has been worried by China's military modernization, especially its double-digit defense spending increase and expanding naval reach.

* The two countries are at odds over China's exploration for natural gas in the East China Sea. In 2008, they agreed on principles to solve the feud by jointly developing gas fields. Progress has been slow and Japan has accused China of drilling for gas in violation of the deal.

Those seas are at the center of a territorial dispute between the two countries focused on a group of uninhabited islets, known as Senkaku in Japan and Diaoyu in China, over which both countries claim sovereignty.

* In September, Japan held a Chinese trawler captain after his boat collided with Japanese coast guard ships near the isles. Beijing canceled diplomatic meetings in protest to Japan's detention of the Chinese trawler captain until he was released.

NORTH KOREA

* China and Japan are both part of stalled six-party talks seeking to end North Korea's nuclear arms program. Japan is more critical of North Korea and joined international condemnation of it over the sinking of a South Korean navy ship in March. China, the North's main diplomatic and economic backer, instead urged restraint by all sides.

(Sources: Reuters, Japanese Cabinet Office, Japanese Finance Ministry, Japanese Foreign Ministry)

(Editing by Robert Birsel and Miral Fahmy)