An American warship sailed near the disputed Paracel Islands in the South China Sea, the US Navy has said, challenging Beijing's claims on the resource-rich waterway and prompting a warning from the Chinese military.

The Thursday operation came a day after China fired ballistic missiles into the sea as part of ongoing live-fire exercises, inflaming already high tensions between Washington and Beijing.

The US regularly conduct "freedom of navigation operations" in the area to challenge Chinese territorial claims. The US Navy's Pacific Fleet said in a statement that the USS Mustin, a guided-missile destroyer, sailed Thursday "in the vicinity of the Paracel Islands to ensure critical shipping lanes in the area remain free and open".

The Chinese military on Friday accused the US ship of entering "China's territorial waters" near the islands "without authorisation". Chinese forces tracked the warship and then warned it to leave, said military spokesman Li Huamin.

In recent years, China has aggressively pursued its territorial claims in the South China Sea, building small shoals and reefs into military bases with airstrips and port facilities. Vietnam, the Philippines, Malaysia and Taiwan also have competing claims in the South China Sea, through which international trade worth trillions of dollars passes a year.

Tensions have risen this week in the area near the Paracel Islands -- called Xisha by Beijing -- where the Chinese military has been conducting exercises. Beijing on Tuesday accused Washington of flying a U-2 spy plane into a no-fly zone to disrupt the drills -- which included the ballistic missile launches.

The Pentagon then accused China of destabilising the region and using the military for "unlawful maritime claims" in a statement criticising the exercises and the use of ballistic missiles in the drills. The Chinese military on Friday said the US had "repeatedly provoked trouble in the South China Sea", urging it to "immediately stop such provocative actions".