The US House speaker, Nancy Pelosi, has said Beijing cannot prevent world leaders from travelling to Taiwan, as she departed from the island on Wednesday to continue her tour of Asia.

In a newly released statement that summarised her trip, Pelosi expressed her admiration for Taiwan’s democracy and criticised China’s ruling Communist party for obstructing Taiwan on the world stage.

“Sadly, Taiwan has been prevented from participating in global meetings, most recently the World Health Organization, because of objections by the Chinese Communist party,” Pelosi said in statement.

“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.”

Pelosi’s trip generated much condemnation from Beijing and sparked fears of a new Taiwan strait crisis. China has vowed “consequences” and announced military exercises in waters around the island on Thursday to show its dissatisfaction. Taiwan said that ahead of the drill 27 Chinese warplanes had entered the island’s air defence zone.

At a press conference on Wednesday, Pelosi questioned the motivations of the Chinese president, Xi Jinping, when asked about his strong response to her visit.

“Its really important for the message to be clear,” said Pelosi. “[The US] is committed to the security of Taiwan … but it’s about our shared values of democracy and freedom and how Taiwan has been an example to the world … Whether there are insecurities of the president of China relating to his own political situation I don’t know.”

Pelosi’s controversial visit has prompted a furious reaction from China, including the scheduling of multiple live-fire exercises, which Taiwan has characterised as a blockade in breach of international law. Taiwan was also apparently targeted by several cyber-attacks, although the perpetrator is unknown. The website of the Taiwan presidential office was hit by a denial-of-service attack, while screens across Taiwan’s ubiquitous 7-Eleven convenience stores were allegedly hacked to display messages in simplified Chinese calling Pelosi a warmonger.

She arrived on Tuesday night and addressed Taiwan’s parliament on Wednesday morning before having a public meeting with President Tsai Ing-wen.

“Our delegation came to Taiwan to make unequivocally clear we will not abandon Taiwan, and we are proud of our enduring friendship,” Pelosi said. Now more than ever, US solidarity with Taiwan was “crucial”.

Pelosi said 43 years ago the US made a “bedrock promise to always stand with Taiwan”. “On this strong foundation we have built a thriving partnership,” she said.

Earlier on Wednesday, Pelosi told Taiwan’s parliament the delegation came “in friendship to Taiwan [and] in peace to the region”.

Pelosi, the US’s first female speaker, praised Taiwan’s growth into a leading democracy, now led by its first female president. She said: “Out of a crucible of challenge you have created a flourishing democracy.”

In her remarks, Tsai said Taiwan would “not back down” in the face of heightened military threats, and would “do whatever it takes to maintain Taiwan’s peace and stability”.

She said Russia’s invasion of Ukraine had made security over the Taiwan strait another focus of the world’s attention.

At the press conference with three selected outlets, Pelosi said China had stood in the way of Taiwan participating in certain meetings, but would not stand in the way of dignitaries coming to visit Taiwan. She said China was making “a big fuss” about this visit because of her status as speaker. “I don’t know if that’s a reason or an excuse,” she added.

“Whatever China will do, they will do in their own good time,” Pelosi said.

Pelosi has spent her decades-long career on trips that she has framed as defending embattled democracies against authoritarian regimes. In 1991, the Democrat and other lawmakers unfurled a pro-democracy banner in Beijing’s Tiananmen Square, two years after China crushed protests there.

China’s government has reacted to Pelosi’s Taiwan visit with outrage. After her arrival, its military announced joint air and sea drills near Taiwan, beginning on Tuesday night and including test launches of conventional missiles in the sea east of Taiwan.

Taiwan’s defence ministry said on Wednesday the live-fire drills around the island this week demonstrated Beijing’s intention to destroy regional peace and stability. It accused China of violating international law with its plans to breach Taiwan’s sovereign space. It said the restrictions on air and sea craft entering the identified zones, some less than 12 miles from Taiwan’s coast and near busy ports, amounted to a blockade.

Taiwan has enhanced alertness levels and will react timely and appropriately to the drills, a defence ministry spokesperson told reporters via a voice message.

At the press conference with Pelosi, Tsai reiterated that Taiwan was committed to maintaining the status quo. “Military exercises are an unnecessary reaction,” she said. “Taiwan has always been open to constructive dialogue.”

China has accused Pelosi of provocation with her visit. On Wednesday afternoon, China’s foreign minister, Wang Yi, told the Asean forum in Cambodia that her trip was a “farce”.

Earlier, Ma Xiaoguang, the spokesperson for China’s Taiwan affairs office of the state council, said Taiwan’s ruling party was “bound to pay an increasingly unbearable price” for hosting Pelosi.

“As for the so-called medal, everyone knows that [former US secretary of state Mike Pompeo], who prides himself on ‘lying, cheating and stealing’ with a bad character, has accepted such medals,” Ma added, referring to Tsai awarding to Pelosi the island’s Order of Propitious Clouds.

Beijing also summoned the US ambassador to China on Tuesday to rebuke him for Pelosi’s “egregious” trip, state media reported. The vice foreign minister, Xie Feng, voiced “strong protests” over Pelosi’s visit to the democratic self-governing island during his talk with ambassador Nicholas Burns.

On the economic front, China suspended the imports of a series of products from Taiwan including citrus fruits and frozen horse mackerel from 3 August, and the commerce ministry suspended China’s export of sand to Taiwan from 3 August.

During her short visit, Pelosi also visited the Jingmei human rights cultural park, a former prison and court complex used during the decades-long period of martial law, when Taiwan was ruled by Chiang Kai-shek. She was expected to meet three political dissidents who had been targeted by China’s government, including the Causeway Bay bookseller Lam Wing-kee, the White Terror prisoner Fred Chin, and Lee Ming-che, who was recently released from a Chinese prison.