(CNN) US Defense Secretary James Mattis said on Tuesday that the United States will continue "a steady drumbeat" of naval exercises to challenge China's territorial claims in the South China Sea, amid Beijing's militarization of the contested waters.

Mattis' comments came after Beijing expressed "firm opposition" on Sunday after two US warships sailed within 12 nautical miles of four artificial islands claimed by China in the disputed Paracel island chain, east of Vietnam.

Speaking to reporters during a flight to Hawaii, Mattis said the South China Sea was international waters and "a lot of nations" wanted to see freedom of navigation maintained in the area.

"There's a very steady drumbeat of freedom of navigation operations ... You'll notice there is only one country that seems to take active steps to rebuff them or state their resentment of them," he said.

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The Chinese government, which claims much of the South China Sea as its sovereign territory, has established a significant military presence in the region, installing radar facilities and airstrips on contested islands and reefs.