NEW YORK TIMES

Taiwan scrambled F-16 fighter jets and dispatched a frigate to the Taiwan Strait on Wednesday after China sent its sole aircraft carrier into the waterway, Taiwan’s official Central News Agency reported.

The transit of the aircraft carrier, the Liaoning, came amid rising tensions between Taiwan and China after President-elect Donald J. Trump broke decades of protocol by speaking on the phone with Taiwan’s president, Tsai Ing-wen, after his election victory. Ms. Tsai leads a political party that has traditionally supported Taiwan’s formal independence from China.

Ms. Tsai, who is visiting Central America this week, made two calls to officials in Taiwan seeking updates on the Liaoning’s transit, the Central News Agency reported, citing Alex Huang, the president’s spokesman. China’s decision to send the carrier through the waterway that separates it from Taiwan reflects an early foreign policy challenge for Mr. Trump.

“It’s a show of force, and I think it is intended in part to intimidate, and that’s worrisome from the U.S. and Taiwan’s point of view because we don’t know how much more they are going to ratchet up these pressures and tensions,” said Bonnie S. Glaser, senior adviser for Asia at the Center for Strategic and International Studies in Washington. “If the Trump administration does see this as a test of U.S. resolve, I suspect they’ll push back pretty forcefully.”

China sent the carrier, which had been conducting exercises in the South China Sea, into the Taiwan Strait on Wednesday morning. Taiwan’s response was the third time in three days that air forces in the region had scrambled jets in response to Chinese military activity, after Japan and South Korea deployed fighters on Monday. Those actions occurred when a squadron of six Chinese bombers and two other aircraft flew over the waters that separate Japan and South Korea and over the Sea of Japan.

Taiwan, considered by Beijing to be Chinese territory, has been governed separately since 1949, when the forces of the Nationalist leader Chiang Kai-shek fled to the island after their defeat on the mainland by the Communists. China views any assertion of Taiwan’s separateness from the mainland — like Ms. Tsai’s call with Mr. Trump — as an affront to its claim of sovereignty.

Since 1979, the United States has recognized the government in Beijing and broke off formal diplomatic ties to Taiwan as part of the One China policy. In the wake of the Trump-Tsai call, China warned the incoming president against making changes to that policy after he takes office on Jan. 20.

Liu Zhenmin, a Chinese vice foreign minister, said on Wednesday that the Taiwan Strait was an international waterway and that it was normal for the Liaoning to pass though it. The passage would not have any effect on cross-strait relations, he said in remarks carried in the Chinese news media.

Mark C. Toner, a State Department spokesman, told reporters in Washington in response to a question about the Liaoning’s passage through the strait that the United States “wouldn’t have a problem” with countries sailing their vessels in international waters as long as it was done in accordance with international law.

It also was not the first time the Liaoning had sailed through the strait: It passed through in November 2013 on its way to the South China Sea after having been commissioned only the year before.

In that instance, the carrier kept to the western half of the strait, closer to mainland China. In a statement on Wednesday morning, Taiwan’s Defense Ministry said that the Liaoning was also staying to the west of the strait’s middle and urged citizens to remain calm. A transit on the eastern side, closer to Taiwan, would be viewed as much more provocative.

Euan Graham, the director of the International Security Program at the Lowy Institute in Sydney, Australia, said that for the Chinese, traveling through the strait was a logical way to move from one area of fleet operations to another along its long coastline. In order for warships based in northern ports, like the Liaoning, to return home from southern waters, they must either pass close to Japanese islands or transit the Taiwan Strait. “Geography forces a very binary choice,” he said.

Mr. Graham said it was important to see how the Liaoning conducted its passage. If it had aircraft on deck and was conducting flight operations, that would be seen as more provocative than if it passed through the strait with the aircraft in its hangar bay, he said.

The Liaoning, commissioned in 2012 and built from a Soviet hull, is China’s first aircraft carrier. In past decades, the United States has shown its resolve to defend Taiwan by sailing carriers through the Taiwan Strait. In 1995, the aircraft carrier Nimitz transited the strait amid heightened tensions after Beijing conducted missile exercises in the waters.

China’s military decision-making is highly secretive, but it would seem inconceivable for the Liaoning to pass through such contested waters without approval from the president, Xi Jinping, who is also the chairman of the Central Military Commission, which controls the military. And the Chinese military media has described the aircraft carrier as embodying Mr. Xi’s plans for a stronger navy, capable of projecting force far beyond China’s territorial waters.

Last Thursday, the front page of People’s Liberation Army Daily, the official newspaper of the Chinese military, featured a report about the aircraft carrier’s latest journey under the headline, “We’re sailing under the leader’s attentive gaze,” a clear tribute to Mr. Xi.

Ma Xiaoguang, a spokesman for the Taiwan Affairs Office in Beijing, said in a news conference on Wednesday that the Liaoning’s passage was part of the ship’s scheduled training in the western Pacific, which had begun on Dec. 24.

Mr. Ma also said that the Taiwan-China relationship in the coming year would face “increasing uncertainty, looming risks and challenges.”

He added that Taiwan’s government and “independence forces” there had “seriously threatened the peace and stability of the Taiwan Strait,” accusing them of engaging in separatist activities and warning that China would “resolutely safeguard its national sovereignty and territorial integrity.”

The aircraft carrier’s passage was part of a cluster of recent acts by the Chinese military that have raised hackles in the region.

Last month, a Chinese warship seized an underwater drone belonging to the United States Navy about 50 miles northwest of Subic Bay in the Philippines. The drone was returned after the Obama administration publicly chided China over the seizure. On Monday, Japan said it had sent fighter jets into the air after Chinese bombers and surveillance planes flew over the East China Sea and the Sea of Japan.

“When China was militarily weaker, Japan considered that area to be its backyard,” said Mr. Ni, the naval researcher. “This was a way of telling Japan that if there ever is conflict, the location of any future battle space won’t be decided by you and America. We have the initiative. So Japan, don’t think of meddling further afield in Taiwan or the South China Sea.”