TAIPEI, Taiwan — The United States’ top health official lauded Taiwan’s democracy and its response to the coronavirus. Taiwan’s president hailed the island’s growing economic and public health ties with the United States.

Yet just offstage from this show of bonhomie Monday between Alex Azar, the secretary of health and human services, and President Tsai Ing-wen of Taiwan was the looming force of China. Beijing claims Taiwan as its territory and underlined its opposition to official exchanges like Azar’s visit by sending two fighter jets toward the island just before the talks.

Azar’s trip, the highest-level visit to Taiwan by a U.S. official since Washington severed official ties with the island in 1979, pointed to the increasingly important role Taiwan will play in a brewing ideological battle between the two superpowers. Taiwan and the United States have frequently framed their alliance as one based on “shared democratic values,” and China’s reaction was a reminder of the risks the island faces as it seeks a stronger relationship with Washington.

To Taiwan, the trip is a diplomatic coup and an opportunity to showcase its widely praised response to the virus, which it achieved despite efforts by China to diplomatically isolate the island. Tsai, in remarks welcoming Azar, said his visit showed that relations between the two sides “have never been better.”

To Beijing, the visit is considered yet another provocation from the United States at the most volatile time in the bilateral relationship in decades. The ruling Communist Party sees the interactions between Taiwan and Washington as a challenge to its sovereignty and in defiance of its threats to unify the island with the mainland by force.

To the Trump administration, Azar’s visit is a chance to take a jab at China, which has sought to spin the coronavirus crisis as a testament to the strength of its authoritarian system. It is a way for Washington to show that it backs Taiwan in the face of increasing efforts by China to keep the island off the international stage.

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“It is a true honor to be here to convey a message of strong support and friendship from President Trump to Taiwan,” Azar said in remarks at the Taiwanese presidential office before heading into a meeting with Tsai. “Taiwan’s response to COVID-19 has been among the most successful in the world, and that is a tribute to the open, transparent, democratic nature of Taiwan’s society and culture.”

As of Monday, Taiwan, an island of 23 million off the southeastern coast of China, had reported just 480 coronavirus cases and seven deaths. Officials have promoted the island as a model of democracy, in part by sending millions of masks labeled “Made in Taiwan” to countries in need.

“Over the last few months, Taiwan and the U.S. have worked together to confront the challenge posed by the COVID-19 pandemic,” Tsai said during the talks with Azar. The two officials wore blue surgical masks as they met.

“When the people of Taiwan saw footage of White House officials wearing ‘Made in Taiwan’ masks, they were happy that these products were helping people in partner countries,” she said.

To critics of the Trump administration, the timing and highly publicized nature of Azar’s visit reflect the government’s desire to distract from its own failed response to the virus. The United States passed a grim milestone over the weekend, with 5 million known cases — by far the most of any country — as well as more than 162,000 deaths from the coronavirus, according to a New York Times database.

Azar’s visit adds to concerns about a new cold war between the United States and China. Tensions have surged between the two powers over geopolitics, human rights, trade and technology. In the past month, there have been fresh clashes over consulates, journalists’ visas and Chinese social networking apps.

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Both countries have in recent months stepped up their military presence in the region, fueling worries about the growing risk of a confrontation, whether intended or not. On Monday, two Chinese fighter jets briefly crossed the median line in the strait separating mainland China and Taiwan. The jets were driven out by patrolling Taiwanese aircraft, Taiwan’s Air Force Command said in a statement released by the defense ministry.

Beijing also lodged a formal complaint with Washington about Azar’s visit, vowing to take countermeasures as it warned the United States not to “gravely damage” relations. There are concerns that as the U.S. election approaches, the Trump administration — which has sought to rally opposition to China as President Donald Trump trails in the polls — could make an overture toward Taiwan that it cannot easily walk back.

“The Chinese side — the whole world — is speculating that Trump could make some even more severe adventures in his China policy to save his prospect of reelection,” including by breaching China’s “very serious bottom line over Taiwan,” said Shi Yinhong, a professor of international relations at Renmin University in Beijing.

China has long been a complicating factor in the United States’ relationship with Taiwan, now one of the most vibrant and prosperous democracies in East Asia.

Concerns about angering Beijing have meant that no sitting Taiwanese president has been allowed to visit Washington. Ties between the United States and Taiwan are managed through quasi-official institutions like the American Institute in Taiwan, which issues visas and provides other basic consular services. The last Cabinet-level visit to Taiwan was a 2014 trip by Gina McCarthy, administrator of the Environmental Protection Agency at the time.

“A lot of what the U.S. does with Taiwan has been so restricted based on Chinese reactions,” said Jessica Drun, a nonresident fellow at the Project 2049 Institute, a nongovernmental organization in Virginia that studies security and policy issues in Asia. “We have become oversensitized to China’s reactions, and they’re aware of this.”

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There are doubts about Trump’s personal commitment to Taiwan. Recently, John Bolton, Trump’s former national security adviser, wrote in his memoir that the president had repeatedly disparaged the island’s significance, comparing Taiwan to the “tip of one of his Sharpies.”

Publicly, Trump and his administration have been far more supportive. In 2016, just before he took office, he broke with nearly four decades of diplomatic practice when he accepted a congratulatory phone call from Tsai. China largely dismissed the call, characterizing it as “a petty action by the Taiwan side.”

In 2018, Trump, over China’s objections, signed the Taiwan Travel Act, which encouraged high-level official visits between the two sides, paving the way for Azar’s visit. The United States remains the island’s top arms supplier, and the administration has approved additional weapons sales to Taiwan.

The U.S. Health and Human Services Department has not said whether Azar will visit an official memorial that has been set up in Taipei for Lee Teng-hui, the former Taiwanese president who led the island’s peaceful democratization. In his remarks, Azar called Lee, who died last month, the “father of Taiwan’s democracy and one of the great leaders of the 20th century’s movement toward democracy.”

As the United States and China dig into a protracted battle, some in Taiwan are concerned that the island’s interests could get lost in the mix.

Chan Chang-chuan, a professor of public health at National Taiwan University, said that one area in which Americans could help Taiwan was in coronavirus-related vaccines and therapeutics. The United States and China are among the countries leading the race to develop a vaccine.

“I do have a very strong wish that Secretary Azar can listen to what we really need,” Chan said. “If we get nothing and China has a vaccine, then it would be like if we didn’t have good weapons to defend our security. It’s strategic.”