"Chinese military took immediate actions by dispatching naval ships and aircrafts to conduct legal identification and verification of the USA warships and warn them off", Wu Qian, defense ministry spokesman, said.
In a statement, the U.S. Pacific Fleet said such operations "challenge excessive maritime claims and demonstrate our commitment to uphold the rights, freedoms, and uses of the sea and airspace guaranteed to all nations under global law".
In a move likely to anger Beijing, the Higgins, a guided-missile destroyer, and the Antietam, a guided-missile cruiser, came within 12 nautical miles of the Paracel Islands in the South China Sea.
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But on this occasion it came amidst a period of heightened tensions between Washington and Beijing, headlined by an ongoing trade dispute and the cancellation of a summit between Donald Trump and North Korean leader Kim Jong Un.
The statement added that sucgh routine and regular operations "are not about one country, nor are they about making political statements".
Washington has slammed China over the moves, and been carrying out "freedom of navigation" patrols in defiance of Beijing.
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China said "mutual trust between the two militaries" had been "harmed" as a result, and that it would "continue to take all necessary measures to defend the country's sovereignty and security".
China has been deploying serious military power to the region - including constructing manmade islands bristling with missiles.
Called "Xisha" in Chinese, the islands have been incorporated into the southern province of Hainan and are being developed for tourism, as well as being equipped with weapon systems meant to enforce China's claim to virtually the entire South China Sea.
The U.S. had included China in the past two versions of the naval exercise known as Rim of the Pacific, or RimPac, in 2014 and 2016.
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Some humanitarian aid from Saudi Arabia and the United Arab Emirates arrived on the island just hours after the cyclone receded. More than 30 people including Indians are missing in Oman since Cyclone Mekunu made landfall on Friday, officials said.