China, which claims democratically ruled Taiwan as its own territory, has repeatedly warned U.S. officials not to meet Tsai, who is on her first U.S. stopover since 2019, seeing it as showing support for the island's desire to be seen as a separate country.
China staged major war games around Taiwan in August when then-U.S. House Speaker Nancy Pelosi visited Taipei. Taiwan's armed forces say they are watching for any Chinese moves when Tsai is abroad.
Tsai is en route to Guatemala and Belize, two of the few countries that recognise Taiwan diplomatically. She will stay in New York until Saturday and will also visit Los Angeles on her return from Central America. She is expected to meet McCarthy in California, although this is not officially confirmed.
"External pressure will not hinder our determination to go to the world," Tsai said before departure at Taiwan's main international airport at Taoyuan.
"We are calm and confident, will neither yield nor provoke. Taiwan will firmly walk on the road of freedom and democracy and go into the world. Although this road is rough, Taiwan is not alone," Tsai said.
Taiwan's de facto embassy in the U.S. confirmed Tsai's arrival in New York on Wednesday afternoon, and said none of her events were open to press or the public during her stopover there. Video clips showed her being greeted in the city by flag-waving supporters.
Taiwan has gradually lost official recognition from more countries as they switch to Beijing. Honduras shifted loyalty on Sunday, leaving just 13 with formal ties with Taiwan. Beijing says Taiwan belongs to "one China" and, as a Chinese province, has no right to state-to-state ties. Taiwan disputes this.
Taiwan is China's most sensitive territorial issue and a major bone of contention with Washington, which, like most countries, maintains only unofficial ties with Taipei. But the U.S. government is required by U.S. law to provide the island with the means to defend itself and it facilitates unofficial stopover visits.
China's Taiwan Affairs Office spokesperson Zhu Fenglian said in Beijing that if Tsai met with McCarthy, China would "definitely take measures to resolutely fight back."
Xu Xueyuan, charge d'affaires at China's embassy in Washington, told reporters such a meeting "could lead to another serious confrontation in the China-U.S. relationship."
"We have made solemn representations to the U.S. side on many occasions and clearly told them that all consequences should be borne by the U.S. side," she said.
The U.S. transit is Tsai's seventh since taking office in 2016 and comes amid concerns in the United States and elsewhere that Russia's invasion of Ukraine might embolden China to move against Taiwan.
A meeting with McCarthy would be the first between a Taiwanese leader and a U.S. House Speaker on U.S. soil, although it is seen as a potentially less provocative alternative to McCarthy visiting Taiwan, something he has said he hopes to do.
Two sources told Reuters that as many as 20 or more U.S. lawmakers planned to accompany McCarthy for his meeting with Tsai, originally set for the Ronald Reagan Presidential Library near Los Angeles. The library has yet to confirm the meeting.
Two other sources said Tsai would attend a banquet with Taiwanese Americans and overseas Taiwanese in New York, as well as an event on Thursday with the Hudson Institute, a think tank to which Taiwan's government is a significant donor, according to its annual reports.
U.S. officials said Tsai would meet Laura Rosenberger, chair at the Washington headquarters of the American Institute in Taiwan (AIT), a U.S. government-run, non-profit organisation that carries out unofficial relations with Taiwan.
Rosenberger, who took up the post last week, was previously a senior official for China and Taiwan on President Joe Biden's National Security Council.
Tsai's transit comes when U.S. relations with China are at what some analysts see as their worst level since Washington normalised ties with Beijing in 1979 and switched diplomatic recognition from Taipei.
White House national security spokesperson John Kirby urged China not to use a "normal" stopover as a pretext to increase aggressive activity against Taiwan.
"We're mindful that things are tense right now" between the United States and China, Kirby said, but he urged Beijing to keep lines of communication open.
Kirby said Washington still wanted to reschedule a trip to Beijing by Secretary of State Antony Blinken that was postponed last month when a suspected Chinese spy balloon was shot down by a U.S. fighter jet.
A senior U.S. administration official told reporters Beijing had stepped up military, economic and diplomatic pressure on Taiwan, but Washington would not alter its "long-standing practice" of facilitating transits through the United States.