The USS Stethem, a guided-missile destroyer, sailed within 12 nautical miles of Triton Island, part of the Paracel Islands in the South China Sea, the official said.
The operation was first reported by Fox News on Sunday.
It was the second "freedom-of-navigation operation," or "fonop," conducted during the presidency of Donald Trump, following a drill in late May in which a US warship sailed within 12 nautical miles of an artificial island built up by China in the South China Sea.
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Twelve nautical miles marks the territorial limits recognised internationally. Sailing within those 12 miles is meant to show that the United States does not recognise territorial claims there.
"Unlike in the Spratlys, where China has created new artificial territory in the last several years, it has effectively controlled the Paracels since 1974," said Mira Rapp-Hooper, a South China Sea expert at the Center for a New American Security. "It claims illegal straight baselines around the Paracels, and the fonop may have been contesting these."
Trump has heaped praise on Chinese President Xi Jinping, but his administration has also stepped up pressure on Beijing as he has become frustrated that China has not done more to pressure North Korea over its nuclear and missile programs.
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On Thursday, the administration imposed sanctions on two Chinese citizens and a shipping company for helping North Korea's nuclear and missile programs, and accused a Chinese bank of laundering money for Pyongyang.
The Trump administration has also approved an arms package for Taiwan worth about $1.4 billion, the State Department said last week. China deems Taiwan its own and has never renounced the use of force to bring the self-ruled island under its control.
Trump is due to speak with Chinese President Xi Jinping and Japanese Prime Minister Shinzo Abe on Sunday, ahead of meetings that he will hold with both leaders on the sidelines of the Group of 20 summit in Hamburg, Germany, next Friday and Saturday.
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