SYDNEY, Feb 22 (Reuters) - An Australian warship sailed through the Taiwan Strait, a government source said on Sunday in the latest transit of the sensitive waterway by a U.S. ally, which Chinese state-backed media said was tracked and monitored by the nation’s military.

In addition to claiming sovereignty over democratically governed Taiwan, Beijing views the narrow, highly strategic strait as Chinese territorial waters and has responded aggressively on occasion to foreign navies sailing there.

The Toowoomba, an Anzac-class frigate of the Royal Australian Navy, “conducted a routine transit through the Taiwan Strait” on Friday and Saturday as part of a “Regional Presence Deployment in the Indo-Pacific region”, the source said.

“All interactions with foreign ships and aircraft were safe and professional,” the source said.

China’s state-backed Global Times newspaper, citing an unnamed Chinese military source, reported late on Saturday that “the Chinese People’s Liberation Army carried out full-process tracking, monitoring, and alert operations throughout the transit.”

U.S. warships traverse the strait every few months, enraging Beijing, and some U.S. allies, such as France, Australia, Britain and Canada, have also made occasional transits.

China has ramped up its military presence around Taiwan and staged its latest war games around the island in late December.

Taiwan’s government rejects Beijing’s sovereignty claims, saying only the island’s people can decide their future.

(Reporting by Sam McKeith in Sydney and Beijing newsroom; Writing and additional reporting by Ben Blanchard in Taipei; Editing by William Mallard)