Taiwan's coast guard said previously that China Coast Guard ships had requested information from three passing commercial vessels, but at the time did not say if they had responded.
Taiwan had informed the ships to ignore the Chinese broadcasts and to contact the Taiwanese coast guard if they needed assistance, the senior official said, as part of efforts to make the international community "understand that China has no jurisdiction here".
The Singapore-flagged vessel operated by Taiwanese shipping giant Evergreen was 39 nautical miles (72 kilometres) southwest of Taiwan's southern tip on June 7 when a China Coast Guard ship contacted it and asked for the number of people on board and their port of destination.
A Chinese crew member cooperated with the request, the official told AFP on the condition of anonymity.
The official said it was the first time that Taiwan's coast guard had heard a China Coast Guard ship asking for information from a foreign commercial vessel in waters around Taiwan.
"On that particular day we broadcast to all cargo ships at the same time telling them not to respond to questions from Chinese government vessels," the official said.
"We heard radio broadcasts to three cargo vessels, but only this one responded, stating which port it was heading to. Later we learned that the person answering the radio was a Chinese crew member."
The official said the Chinese national -- one of 15 Chinese among 21 crew members -- may have felt compelled to answer out of "fear" of the Chinese government, or it was possible that "they coordinated in advance" with the coast guard.
The other two ships -- operating under Liberian and Benin flags -- were off Taiwan's east coast when they were contacted by the China Coast Guard on June 9, but they did not comply.
- 'Cognitive warfare' -
Chinese state media said previously that last month's "law enforcement operation" involving Chinese ships near Taiwan was in response to talks between Japan and the Philippines to draw a boundary in waters to the east of the island.
China, which asserts Taiwan is part of its territory, called the talks "illegal" and has claimed exclusive control over the waters.
Taiwan branded the Chinese operation as "provocative" and "expansionism in disguise".
The British, German and French representative offices in Taipei also expressed concern over the "novel Chinese activity".
The official said Taiwan deployed eight coast guard ships to shadow eight Chinese coast guard and other government vessels during the operation.
China has ramped up military pressure on Taiwan in recent years and carried out multiple large-scale exercises.
While the risk of an invasion or blockade of Taiwan is a constant threat, analysts have also warned that China could use a law enforcement-led quarantine to control commercial shipping around the island.
But the official dismissed concerns that China could impose full control on waters to the east of Taiwan.
"From our current perspective it won't reach that level. The eastern sea area is simply too vast," the official said.
"In reality, they're using these actions to claim to the outside world that they exercise jurisdiction over waters east of Taiwan's east coast. This is typical cognitive warfare."
The official said previous Chinese activity in those waters had been "sporadic", but was now "more frequent and intensified".