Factbox: Ties between China and Japan

(Reuters) - Japan faces a dilemma over how to engage with China as deepening economic ties jostle for priority with anxiety over the rising Asian power's military reach.

Below are some key facts about Sino-Japanese relations.

ECONOMIC POWERHOUSES, SHIFTING RANKINGS

Preliminary statistics indicate that 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 GDP totaled $1.2883 trillion on a nominal dollar basis, against China's second-quarter unadjusted GDP of $1.3369 trillion.

The GDP of Japan and China combined account for about 17 percent of the world's total output.

China-Japan trade rebounded in the first half of 2010 after slumping in the global financial crisis. The two countries' bilateral trade reached 12.6 trillion yen ($149.2 billion) in value in the first half, a jump of 34.5 percent on the same time last year, according to Japanese statistics. Two-way trade between China and Japan 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 have hit Japanese firms in recent months, including suppliers to Toyota Motor Corp (7203.T) and Honda Motor Corp (7267.T).

HISTORICAL TENSIONS

Japan invaded and occupied much 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 decried high-profile visits to Tokyo's Yasukuni Shrine for 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, prime minister from 2001 to 2006, made annual visits to the shrine while in office. His successors have stayed away from the controversial shrine.

TAIWAN, NORTH KOREA

China wants Japan to clearly back Beijing's "one China" policy. Japan says it accepts that, but many politicians and businesses have close ties with Taiwan, a former Japanese colony.

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

TERRITORIAL DISPUTES AND MILITARY TENSIONS

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, though talks are continuing.

Tokyo and Beijing claim sovereignty over a group of East China Sea islets, known as Senkaku in Japan and Diaoyu in China.

Japan has been worried by China's military modernization, especially its double-digit defense spending and expanding naval reach. In May, Tokyo lodged a protest with Beijing, claiming a Chinese ship had violated Japan's sovereign rights by approaching a Japanese survey vessel.

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

($1 = 84.45 Yen)

(Reporting by Chris Buckley and Yoko Kubota; Editing by Sugita Katyal)