The Arleigh Burke-class guided-missile destroyer USS Milius (DDG-69), deployed to the US 7th Fleet area of operations, conducts underway operations, at an undisclosed location in South China Sea. Reuters

China condemned on Monday the "illegal" intrusion of a US warship into waters it claims in the South China Sea, after the US Navy said its guided-missile destroyer the USS Milius had sailed through the area.

"Missile destroyer USS Milius illegally intruded into the waters adjacent to the Meiji Reef in China's Nansha Islands without the approval of the Chinese government," Tian Junli, spokesman for the Chinese military's Southern Theatre Command, said in a statement, adding Beijing's air force "followed and carried out surveillance of the vessel".

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Meanwhile, the US Navy said its guided-missile destroyer the USS Milius sailed through waters claimed by Beijing in the South China Sea in a "freedom of navigation" operation on Monday.

The operation "upheld the rights, freedoms, and lawful uses of the sea", the Navy said in a statement.

The Arleigh Burke-class guided-missile destroyer USS Milius conducts underway operations. Reuters

The destroyer had "asserted navigational rights and freedoms in the South China Sea near the Spratly Islands, consistent with international law", it added.

After the operation, the Milius "exited the excessive claim area and continued operations in the South China Sea", it said.

According to the statement, the ship sailed within 12 nautical miles of Mischief Reef — about 1,400 kilometres (860 miles) from the southern tip of Taiwan's mainland.

Chinese fighter jets and warships are carrying out three days of military drills around Taiwan, including simulated strikes on the island.

The war games follow a meeting last week between Taiwanese President Tsai Ing-wen and US House Speaker Kevin McCarthy outside Los Angeles.

China's exercises sparked condemnation from Taipei and calls for restraint from Washington, which said it was "monitoring Beijing's actions closely".

On Monday, Beijing said fighter jets carrying "live ammunition" had conducted "simulated strikes" near Taiwan and that its Shandong aircraft carrier was involved in the ongoing exercises.