The McCain's activities near the Paracels come just one day after the warship sailed through the Taiwan Strait, an global waterway where China unlawfully expects foreign ships to seek permission before transiting the area.
The United States has urged China to end its military, diplomatic, and economic pressure against Taiwan, State Department spokesperson Ned Price said.
The US Navy's Seventh Fleet says the destroyer conducted a routine Taiwan Strait transit on Thursday, local time.
The People's Liberation Army "organised naval and air forces to track, monitor and warn off" the warship, the Chinese military said, blasting the USA for "seriously violating China's sovereignty" and "harming regional peace".
He said US alliances and partnerships were a "force multiplier across any range of challenges, and that includes in our relationship with Beijing".
President Biden said on Thursday the U.S. will confront China's "coercive" and "aggressive" actions.
The U.S. showed a strong commitment to Taiwan's defense during former president Donald Trump's administration by approving the sale of sophisticated military hardware to Taipei, including F-16 fighter jets, advanced missiles and main battle tanks, while sending high-level envoys to the island.
Foreign ministry spokesman Wang Wenbin on Thursday said Beijing is closely watching the movements of the U.S. Navy amid the warship's operation, according to a report from the South China Morning Post.
On Wednesday, the Biden administration said that the USA continues to adhere to "One China" policy notwithstanding tensions between Washington with Beijing and the close relations the United States continues to foster with Taiwan.
Surveying 1,040 people in December 2020, the poll found 69% of voters believed if China takes more action to address climate change then the United States should follow suit.
During the last month of the Trump administration, Secretary of State Mike Pompeo also said the US was lifting the "self-imposed restrictions on the US-Taiwan relationship", further raising tensions between Washington and Beijing.
Biden's nominee for United Nations ambassador, Linda Thomas-Greenfield, last week called China "a strategic adversary" that threatens the world and expressed regret for a speech she gave in 2019 that praised China's initiatives in Africa and made no mention of its human rights abuses.