TOKYO, May 16 (Reuters) - Warships from France, Japan, Australia and the United States held their first ever combined naval exercise on Thursday, in a new show of force in Asian waters by the United States and its allies who are wary of China's growing power.

The French aircraft carrier, FS Charles de Gaulle and its escorts, were joined the Bay of Bengal by five other naval vessel, including a Japanese helicopter carrier, a U.S. guided missile destroyer and an Australian submarine.

They practiced formation sailing, live fire drills, and search and rescue, according to a news release from the U.S. Seventh Fleet.

As China's military power grows in the region, the United States and Japan are looking to forge stronger defense ties with other countries in the Asia-Pacific region and beyond, including France and the Britain, that could help counterbalance China's expanding influence.

The Japanese carrier the Izumo and the U.S. destroyer, the USS William P. Lawrence, last week joined vessels from India and the Philippines for exercises in the South China Sea, most of which China claims.

Those maneuvers in waters through which around a third of the world's maritime trade flows, came after two other U.S. warships sailed near islands in the region claimed by China, prompting a protest from Beijing.

China claims almost all of the strategic South China Sea with Brunei, Indonesia, Malaysia, the Philippines, Taiwan and Vietnam pushing competing claims to parts of it.

The United States, Japan, France and Australia do not have any territorial claims there. (Reporting by Tim Kelly; Editing by Michael Perry)