The destroyer, however, did not violate the 12-nautical-mile territorial limits of the islands, according to a Reuters report, citing U.S. military officials.
"China will continue to take resolute measures to protect Chinese sovereign territory and maritime interests", Chinese Foreign Ministry spokeswoman Hua Chunying said.
The Chinese spokesperson said the USA warship violated Chinese and worldwide laws and seriously threatened China's sovereignty and security.
Turning to the North Korean nuclear threat, Noh said, "Bilateral cooperation is more important than ever under the shared view that North Korea's nuclear weapons and missiles pose obstacles to achieving peace in northeast Asia and the national interests of South Korea and China".
"We demand the USA side earnestly take steps to correct its mistakes", the ministry said in a statement.
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It added that it would further strengthen its naval and air defenses. Beijing accuses the U.S. of violating its sovereignty, while Washington claims the missions support "freedom of navigation" in the region. China is North Korea's neighbor and biggest trading partner.
Twelve nautical miles mark internationally recognized territorial limits.
China claims nearly all of the South China Sea, and has heavily militarized some islands in the region and expanded other territories with major land reclamation work, turning sandbars into islands and equipping them with airfields, ports and weapons systems.
China's Foreign Ministry has also urged the United States to "respect the sovereignty and security" of the country and stop such "erroneous acts".
Trump's visit to China will reciprocate a trip to the United States made in April by Chinese President Xi Jinping.
The incident comes as USA officials are pressing China to use more economic and diplomatic pressure on North Korea to prevent further military escalation in the region.