Three Chinese warships had sailed in waters surrounding the self-ruled island, while a fighter jet and an antisubmarine helicopter also had crossed the island's air defense identification zone, Taiwan's Defense Ministry said.

On Wednesday, China's Shandong aircraft carrier, one of two in its naval fleet, sailed through Taiwan's southeastern waters on its way to the western Pacific, hours before Tsai met McCarthy in Los Angeles, California, the US.

Beijing, which views Taiwan as part of its territory, had repeatedly warned against the meeting, and reiterated on Thursday it would take "forceful measures to firmly safeguard national sovereignty".

Tsai told reporters her government was committed to ensuring "the free and democratic way of life of the people of Taiwan" before she left Los Angeles, where she was stopping on her way back from Latin America.

"We also hope to do our best to maintain peace and stability between the two sides," she added.

Last August, China deployed warships, missiles and fighter jets around Taiwan for its largest show of force in years following a trip to the island by McCarthy's predecessor Nancy Pelosi.

Its response to the Tsai-McCarthy meeting has so far been on a much lower level, but still left Taiwan on alert.

Premier Chen Chien-jen said on Friday Taiwan's defense and security agencies had been keeping a close eye on developments, and asked "the public to rest assured".

On Thursday, the defense ministry said three warships had been detected around the Taiwan Strait and one Chinese naval helicopter crossed the island's ADIZ.

The display prompted calls from the US asking China "to cease its military, diplomatic and economic pressure against Taiwan and instead engage in meaningful diplomacy".

"We remain committed to maintaining open channels of communication so as to prevent the risk of any kind of miscalculation," State Department spokesman Vedant Patel told reporters.

McCarthy, who is second in line for the US presidency, had originally planned to go to Taiwan himself but opted instead to meet Tsai in California.

The decision was viewed as a compromise that would underscore support for Taiwan but avoid inflaming tensions with China, a move analysts say had so far proven successful.

Tsai said on Thursday it was "quite common for us to meet our US friends during transits”, she said.

"I also hope the Chinese side can exercise self-restraint and don't overreact."

McCarthy had vowed US arms sales to Taiwan, which infuriated Chinese leadership, would continue, in what he said was a proven strategy to dissuade aggression.

"And what we know through history, the best way to do that is supply the weapons that allow people to deter war," he said.

"It is a critical lesson that we learned through Ukraine, that the idea of just sanctions in the future is not going to stop somebody" who wants to wage war.

Tsai acknowledged the weapons deal on Thursday but did not provide further details.

"We have purchased arms from the US and we hope the arms will be delivered on time," she said.

On Friday, China slapped sanctions on Taipei's de facto ambassador to the US, Hsiao Bi-khim, banning her from entering China and accusing her of "deliberately inciting cross-strait confrontation".

Beijing's foreign ministry also announced sanctions against the Hudson Institute, a Washington-based conservative think-tank, as well as the Ronald Reagan Presidential Library, for "providing a platform and facilitating Tsai Ing-wen's engagement in 'Taiwan separatism' activities in the United States".

The two organizations are now barred from engaging in transactions and cooperation with Chinese entities, while four individuals linked to them are blocked from entering or conducting business in China.