The Chinese military said it warned a US warship to "leave" waters in the disputed South China Sea on Thursday, claims swiftly denied as "false" by American forces.

China claims sovereignty over almost the entire South China Sea -- a strategic waterway through which trillions of dollars in trade pass annually -- despite an international court ruling that the assertion has no legal basis.

The Philippines, Vietnam, Malaysia and Brunei all have overlapping claims in the sea, while the United States sends naval vessels through it to assert freedom of navigation in international waters.

The Southern Theater Command of China's People's Liberation Army (PLA) said the USS Milius, a guided missile destroyer, on Thursday entered waters around the Paracel Islands, which are also claimed by Vietnam.

The PLA "organised sea and air forces to track and monitor (the ship) in accordance with the law" and "warned it to leave", spokesman Tian Junli said.

The vessel "made an illegal incursion into Chinese territorial waters... without permission from the Chinese government, harming peace and stability" in the region, he said.

The US military swiftly denied the claims, telling AFP that "the PRC's statement is false", using the acronym for the People's Republic of China.

The vessel "is conducting routine operations in the South China Sea and was not expelled", said a spokesperson for US Indo-Pacific Command.

"The United States will continue to fly, sail, and operate wherever international law allows," the spokesperson said.

While asserting their claims in the South China Sea, Chinese authorities in recent years have built artificial islands, including some with military facilities and runways.

Regional nations have also accused Chinese vessels of harassing their fishing boats.