JAKARTA (Reuters) - Indonesia's air force is holding its largest military exercise this week, near some of its islands in the South China Sea, in a show of sovereignty over the gas-rich area on the fringe of territory claimed by China, officials said on Tuesday.

President Joko Widodo in June launched an unprecedented campaign to bolster fishing, oil exploration and defense facilities around the Natuna island chain after a series of face-offs between the Indonesian navy and Chinese fishing boats.

China, while not disputing Indonesia's clams to the Natuna islands, has raised Indonesian anger by saying the two countries had "over-lapping claims" to waters near them, an area Indonesia calls the Natuna Sea.

"We want to show our existence in the area. We have a good enough air force to act as a deterrent," said Jemi Trisonjaya, spokesman for Indonesia's air force.

More than 2,000 air force personnel were taking part in the two-week long exercise, which includes the deployment of Indonesia's fleet of Russian Sukhoi and F-16 fighter jets, he said.

Other branches of the Indonesian armed forces are not taking part in exercise, which ends on Thursday.

China claims almost the entire South China Sea, where about $5 trillion worth of trade passes every year. Brunei, Malaysia, the Philippines, Taiwan and Vietnam also have claims.

While Indonesia is not part of the dispute over claims in the South China Sea, it objects to China's inclusion of waters around the Natuna Islands within its "nine-dash line", a demarcation line used by China to show its claims in the sea.

(Reporting by Agustinus Beo Da Costa; Writing by Randy Fabi; Editing by Robert Birsel)