China asserts that Taiwan is part of its territory and claims legal jurisdiction over waters surrounding it, which Taipei rejects.
Tensions in the waters to the east of Taiwan have risen in recent weeks after Chinese coast guard and other government ships carried out an operation.
Chinese state media said previously it was in response to talks between Japan and the Philippines to draw a boundary in those waters.
China has called the talks "illegal" and claimed exclusive control over the waters.
Taiwan branded the Chinese operation as "provocative" and "expansionism in disguise".
China Coast Guard (CCG) spokesman Jiang Lue said Saturday that a task force group led by the CCG's Xiushan ship formation had replaced another such group "to continue law enforcement patrols" in waters east of Taiwan.
Taiwan's coast guard said it had deployed two vessels to "sail alongside and monitor" two Chinese ships, including the Xiushan, which were about 54 nautical miles (100 kilometres) off its coast.
"Taiwan possesses sovereign rights and jurisdiction over the Exclusive Economic Zone east of Taiwan, whereas China has absolutely no sovereign rights over any waters surrounding Taiwan," Taiwan's coast guard said in a statement.
"China's attempts to harass through maritime navigation cannot alter this indisputable fact."
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.
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