BEIJING (REUTERS) - China's military said on Wednesday (Aug 19) that the latest US navy sailing near Chinese-claimed Taiwan was "extremely dangerous", and stirring up such trouble was in neither country's interests.

The US guided-missile destroyer USS Mustin sailed through the narrow and sensitive Taiwan Strait on Tuesday, the US navy said, in what have become relatively routine trips in recent months, though they always anger China.

The Eastern Theatre Command of China's People's Liberation Army said its air and naval forces followed and monitored the US ship throughout its voyage.

"Any words or deeds that... cause trouble in the Taiwan Strait are not in line with the fundamental interests of China and the United States, harm the well-being of compatriots on both sides of the strait, pose real threats to peace and stability in the region and are extremely dangerous," it said.

Chinese forces will remain on high alert at all times to safeguard China's sovereignty and territorial integrity, it added.

Taiwan's defence ministry said the US ship was on an "ordinary mission" and passed through the Taiwan Strait in a southerly direction.

The sailing comes a week after US Health Secretary Alex Azar visited Taiwan, the highest-level US official to travel to the island since Washington broke off diplomatic ties with Taipei in favour of Beijing in 1979.

China responded by sending fighter jets close to Taiwan.

China considers Taiwan a purely domestic matter, and routinely calls it the most sensitive and important issue in its relations with the United States.