"The Eastern Theatre Command of China's PLA organised naval and air forces to trail their entire course and stand alert in accordance with laws and regulations," said Senior Colonel Shi Yi, referring to the People's Liberation Army.

"Troops in the theatre remain on constant high alert, and will resolutely protect national sovereignty and security as well as regional peace and stability," Shi said in a statement.

Shi said that the two ships -- identified in the statement only as "Johnson" of the United States and "Ottawa" of Canada -- had "openly hyped up" their passage through the waters.

Taiwan lives under constant threat of an invasion by China, which claims the self-ruled island as part of its territory to be taken back, by force if necessary.

Washington diplomatically recognises Beijing over Taipei but maintains de facto relations with democratic Taiwan and supports the island's right to decide its own future.

The United States and Western allies have increased "freedom of navigation" crossings by naval vessels of both the Taiwan Strait and the disputed South China Sea to reinforce that both are international waterways, angering Beijing.