Japan's top government spokesman Yoshimasa Hayashi declined to comment on the reports at a regular briefing because they concern military operations.
But Beijing confirmed its military had responded to "the activities of a Japanese Self-Defence Force ship entering the Taiwan Strait".
"China is highly vigilant about the political intentions of Japan's actions and has lodged stern representations with Japan," Foreign Ministry spokesman Lin Jian said.
The United States and its allies are increasingly crossing the 180km Taiwan Strait to reinforce its status as an international waterway, angering China.
The Sazanami destroyer made the unprecedented passage on Sept 25, several Japanese media outlets said.
Military vessels from New Zealand and Australia also sailed through the fiercely contested waterway on the same day, Wellington's Defence Ministry said on Sept 26.
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