"The relevant action by the USA vessel violated Chinese laws and relevant global laws, infringed upon China's sovereignty, and undermined peace, security and order of the relevant waters", Lu said.
Officials from both countries are meeting in China this week in the first face-to-face interaction they've had since last November, when they agreed to a 90-day cease-fire in their trade dispute.
Since the two presidents met on December 1, China has made a number of concessions to US demands, including temporarily cutting punitive tariffs on USA -made cars, resuming soybean purchases, promising to open up its markets for more foreign investment, and drafting a law to prevent forced technology transfers.
Asian stocks markets jumped after the talks were extended for an unscheduled third day, fuelling optimism that the world's largest economies can strike a trade deal to avoid an all-out confrontation that would severely disrupt the global economy.
Chinese Foreign Ministry spokesman Lu Kang said China had made "stern complaints" with the United States about the sighting of the destroyer, but the trade talks went ahead as scheduled. The move prompted China to increase tariffs on Dollars 110 billion of U.S. goods.
U.S. Trade Representative Robert Lighthizer, who Trump appointed to lead the China talks, is pressing for the U.S.to take a harder line in the negotiations.
"It is imperative for the two sides to create enabling environment for the talks at this time", he said. "China has the good faith, on the basis of mutual respect and equality, to resolve the bilateral trade frictions".
"As for whether the Chinese economy is good or not, I have already explained this".
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Trump imposed import tariffs on hundreds of billions of dollars of Chinese goods a year ago and has threatened more to pressure Beijing to change its practices on issues ranging from industrial subsidies to intellectual property to hacking.
Since March, the USA has slapped tariffs on $250 billion worth of Chinese goods, while China has placed a series of retaliatory tariffs on US goods totaling $110 billion.
Even so, Lu said, "China's development has ample tenacity and huge potential".
And onto the latest on the trade talks between the world's two superpowers. The Chinese side has suggested talks were "constructive".
A member of the US trade delegation to China, carries a folder as he leaves a hotel in Beijing, Jan. 7, 2019.
Another photo shows a wider view of dozens of officials from each country seated at three long tables facing each other and around the room's borders, significantly more people than those attending previous rounds of U.S.
China claims nearly all of the strategic South China Sea and frequently attacks the USA and its allies for carrying out freedom of navigation naval operations near the Chinese-occupied islands.
The Trump administration's calculus regarding how much to stress either increased purchases of United States goods, on the one hand, or structural reforms reflects a divide within the White House.