US House of Representatives Speaker Nancy Pelosi has left Taiwan after touting its democracy and pledging American solidarity during her brief visit, adding that Chinese anger cannot stop world leaders from travelling to the self-ruled island claimed by Beijing.

China demonstrated its outrage over the highest-level US visit to the island in 25 years with a burst of military activity in surrounding waters, summoning the US ambassador in Beijing and halting several agricultural imports from Taiwan.

Some of China's planned military exercises were to take place within Taiwan's 12 nautical mile sea and air territory, according to Taiwan's defence ministry, an unprecedented move that a senior defence official described to reporters as "amounting to a sea and air blockade of Taiwan".

Taiwan scrambled jets today to warn away 27 Chinese aircraft in its air defence zone, the island's defence ministry said, adding that 22 of them crossed the median line separating the island from China.

Ms Pelosi arrived with a congressional delegation on her unannounced but closely watched visit late last night, defying China's repeated warnings, on a trip that she said demonstrated unwavering US commitment to Taiwan's democracy.

How is China punishing Taiwan for the Pelosi visit?

"Our delegation came to Taiwan to make unequivocally clear that we will not abandon Taiwan," Ms Pelosi told Taiwan's President Tsai Ing-wen, who Beijing suspects of pushing for formal independence - a red line for China.

"Now, more than ever, America's solidarity with Taiwan is crucial, and that's the message we are bringing here today," Ms Pelosi said during her roughly 19-hour visit.

A long-time China critic, especially on human rights, and a political ally of US President Joe Biden, Ms Pelosi met with a former Tiananmen activist, a Hong Kong bookseller who had been detained by China and a Taiwanese activist recently released by China.

The last US House speaker to go to Taiwan was Newt Gingrich in 1997. Ms Pelosi's visit comes amid sharply deteriorating US-Chinese relations. During the past quarter century, China has become a far more powerful economic, military and geopolitical force.

China considers Taiwan part of its territory and has never renounced using force to bring it under its control. The United States and the foreign ministers of the Group of Seven nations have warned China against using the visit as a pretext for military action against Taiwan.

"Sadly, Taiwan has been prevented from participating in global meetings, most recently the World Health Organization, because of objections by the Chinese Communist Party," Ms Pelosi said in statement issued after her departure.

Nancy Pelosi and President Tsai Ing-wen bump elbows as they greet each other

"While they may prevent Taiwan from sending its leaders to global forums, they cannot prevent world leaders or anyone from travelling to Taiwan to pay respect to its flourishing democracy, to highlight its many successes and to reaffirm our commitment to continued collaboration," Ms Pelosi added.

She later arrived in South Korea, according to local media.

China's customs department announced a suspension of imports of citrus fruits and certain fish - chilled white striped hairtail and frozen horse mackerel - from Taiwan, while its commerce ministry banned export of natural sand to Taiwan.

Military drills

China's military announced joint air and sea drills near Taiwan and test launches of conventional missiles in the sea east of the island, with Chinese state news agency Xinhua describing live-fire drills and other exercises around Taiwan from Thursday to Sunday.

China's foreign ministry said that Ms Pelosi's visit damages peace and stability in the Taiwan Strait, harms the political foundation of US-Chinese relations and infringes upon China's sovereignty and territorial integrity.

US Secretary of State Antony Blinken discussed the potential for Ms Pelosi's visit with counterpart Wang Yi during a G20 meeting in Bali last month, and said any such trip would be entirely Ms Pelosi's decision and independent of the Biden administration, a senior US official has said.

People gathered outside the Grand Hyatt hotel in Taipei in support of Nancy Pelosi's visit

The State Department confirmed that China delivered a formal protest to US Ambassador Nicholas Burns in Beijing, and that Mr Burns reiterated US readiness to work with China to prevent escalation and keep lines of communication open.

The United States has no official diplomatic relations with Taiwan but is bound by American law to provide it with the means to defend itself. China views visits by US officials to Taiwan as sending an encouraging signal to the pro-independence camp on the island. Taiwan rejects China's sovereignty claims, saying only the Taiwanese people can decide the island's future.

Taiwan's military increased its alertness level. Its defence ministry said China was attempting to threaten key ports and cities with drills in the surrounding waters.

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Pelosi visit to Taiwan 'will have consequences'

China's Ambassador to Ireland described Ms Pelosi's visit to Taiwan as "reckless" and warned it will have consequences.

Speaking on RTÉ's Morning Ireland, He Xiangdong did not specify what the consequences would be but said the Chinese government and the Chinese Ministry of Defence will react to the visit, which he said sends "a very wrong signal to Taiwan independence separatist forces".

"China has every right to defend its sovereignty and territorial integrity. And we are fully justified to do what we must. The current situation is created purely by the US side and separatist forces in Taiwan, so of course they have to bear the responsibility and the consequences," Mr He said.

The ambassador said Taiwan is part of China and the "Taiwan question" is not an international issue, but rather a national one that will be solved by China achieving reunification.

He said China "will do our outmost with maximum sincerity to achieve a peaceful unification".

"We strive for peaceful reunification with Taiwan, while we are also determined to safeguard our sovereignty and territorial integrity, we will not sit idly and will have to make legitimate and necessary responses and the event of employing any non-peaceful means and other necessary measures."

Mr He added that China will do its upmost "to protect the lives, property and all other legitimate rights and interests of the Taiwanese people because they are Chinese people".

Former US national security advisor John Bolton

Former US national security advisor John Bolton has said that it was the right decision for Ms Pelosi to go to Taiwan.

Mr Bolton said: "I think she was right to go. I think no time is convenient for China, given their position on Taiwan".

He said that Americans have been committed to the defence of Taiwan since 1979 and see it as "an American ally".

Speaking to RTÉ's Drivetime, Mr Bolton said: "Nobody tells us where our leaders go, we make our own foreign policy and if Beijing doesn't like it well that is just too bad."

He added: "If a senior American official or even a private citizen wants to go to Taiwan, that's their right."