The Liaoning and accompanying vessels entered Taiwan's air defence zone on Tuesday, the same day Chinese President Xi Jinping delivered a blistering nationalistic speech -- warning against what he called any attempts to split China.

"All acts and tricks to separate the country are doomed to fail and will be condemned by the people and punished by history," Xi said in a speech ending the annual session of the National People's Congress.

But a senior US official -- visiting the island despite protests from Beijing -- said Wednesday that his country's willingness to defend Taiwan's democracy had never been stronger.

China, which sees self-ruled Taiwan as its own territory, has stepped up air and naval patrols around the island since Beijing-sceptic President Tsai Ing-wen came to power in May 2016.

She refuses publicly to accept the "One China" formula agreed between Beijing and Taiwan's previous government.

Chinese warplanes conducted 25 drills around Taiwan between August 2016 and mid-December last year, according to Taipei.

China is also angry at President Donald Trump's signing of new rules allowing top-level US officials to travel to Taiwan.

The first such visitor since then, Deputy Assistant Secretary of State Alex Wong, expressed his country's support for Taipei when he attended a business dinner alongside President Tsai on Wednesday evening.

"Taiwan can no longer be excluded unjustly from international fora... that is why it's US policy to promote appropriate respect and treatment for Taiwan's role in the world," Wong said in reference to Beijing's efforts to restrict Taipei's international role.

"As reflected in the US National Security Strategy, we wish to strengthen our ties with the Taiwan people and to bolster Taiwan's ability to defend its democracy. Our commitment to these goals has never been stronger.

"The United States has been, is, and always will be Taiwan's closest friend and partner," Wong said.

China's foreign ministry lodged an official protest with Washington over the visit.

"We urge the United States to abide by the One China principle," ministry spokeswoman Hua Chunying told a regular briefing in Beijing.

She called on Washington to "stop any form of official exchanges and contacts with Taiwan, and prudently and properly handle Taiwan-related issues, so as to avoid serious damage to Sino-US relations and peace and stability in the Taiwan Strait".

The Liaoning, China's sole operational aircraft carrier, left around noon Wednesday, Taiwan's defence ministry said.

The Soviet-built ship caused a stir in Taiwan when it first entered the strait in January last year in what was seen as a show of strength by Beijing.

It sailed past Taiwan again last July en route to Hong Kong and returned in January this year.

Taipei's defence ministry said no unusual activities by the carrier group had been spotted "and we urge the public to rest assured".

China still sees Taiwan as part of its territory awaiting reunification, by force if necessary, even though the two sides split in 1949 after a civil war and have been ruled separately ever since.