Taiwan's President Tsai Ing-wen rejected China's "one country, two systems" model and said that both sides need to find "a way to coexist."
"Cross-strait relations have reached a historical turning point. Both sides have a duty to find a way to coexist over the long term and prevent the intensification of antagonism and differences," Tsai said at her inauguration on Wednesday.
"We will not accept the Beijing authorities' use of 'one country, two systems' to downgrade Taiwan and undermine the cross-strait status quo. We stand fast by this principle," Tsai added. She also pledged to "engage in dialogue with China."
Mainland China claims Taiwan as a province with no right to its own diplomatic representation. The Chinese Communist Party has never ruled over self-governed Taiwan.
In response to Tsai, China's Taiwan Affairs Office said that "reunification" of Taiwan with the mainland is a "historical inevitability" which "cannot be stopped by anyone or by any force," state news agency Xinhua reported.
China "will never tolerate any act of splitting the country, and will not tolerate any external forces interfering in China's internal politics," reported Xinhua citing Taiwan Affairs Office spokesperson, Ma Xiaoguang.
The relationship between Beijing and Taipei has been frosty since Tsai, a politician from the independence-leaning Democratic Progressive Party, took office in 2016. China cut off official dialogue with Taiwan after she won her first election.
Beijing has also actively pursued Taiwan's few allies, persuading them to switch diplomatic ties to China instead.
Most recently, Beijing opposed Taiwan's participation as an observer in an important World Health Organization meeting. Taiwan had been lobbying to join the meeting, saying it wants to share its success in containing the coronavirus outbreak.
"Faced with changing circumstances, I will hold firm to my principles, adopt an open attitude to resolve issues, and shoulder my responsibilities as president," Tsai said, according to an official translation of her speech.
"I also hope that the leader on the other side of the Strait will take on the same responsibility, and work with us to jointly stabilize the long-term development of cross-strait relations," Tsai added, referring to Chinese President Xi Jinping.
After a resounding victory in January's elections, Tsai heads into her second and final term in office with a strong mandate.
Capitalizing on Taiwanese fears about eroding freedoms if they voted for a leader who was China-friendly, she supported protesters in Hong Kong to highlight concerns about Beijing's encroaching pressure on civil liberties in the territory, a Chinese special administration region.
After her re-election, China ramped up its military drills around the island.
"In the face of complex and changing cross-strait circumstances, we have made the greatest effort to maintain peace and stability in the Taiwan Strait over the past four years, gaining approval from the international community," Tsai said during her inauguration speech in Taipei.
"We will continue these efforts, and we are willing to engage in dialogue with China and make more concrete contributions to regional security," she said.
China's pressure on Taiwan will only increase, said Michael Boyden, managing director at Taiwan Asia Strategy Consulting.
Taiwan will have to find a way to have constructive talks with China in the next four years under Tsai's leadership, as the pressure on Taipei — whether it's economic, military or diplomatic — "is only going to intensify in my opinion," Boyden told CNBC's "Street Signs" on Wednesday.
And Xi may be "president for life, but he is not immortal," he pointed out. "He wants to be the Chinese leader who resolves the Taiwan issue. He certainly does not want to be the Chinese leader who let Taiwan slip away, so the pressure is only going to intensify."
Even though ideology has always trumped economics for the DPP, Tsai's administration should find a way to engage in talks with Beijing, Boyden said.
That is as Taiwan's export reliant economy is going to suffer this year due to the fallout from the coronavirus outbreak. Taiwan posted 1.54% GDP growth in the first quarter of 2020 — its weakest in nearly four years. China is Taiwan's largest trading partner.
Tsai's success at the polls point to Taiwanese endorsement of her stance toward the island's relationship with China. Younger generations in particular see themselves as Taiwanese — rather as both Taiwanese and Chinese — in terms of national identity, according to a recent Pew Research Center survey.
On Wednesday, Tsai said Taiwan will keep working at developing its international relationships.
"Over the next four years, we will continue to fight for our participation in international organizations, strengthen mutually beneficial cooperation with our allies, and bolster ties with the United States, Japan, Europe, and other like-minded countries," she said.
U.S. Secretary of State Mike Pompeo on Tuesday congratulated Tsai on her inauguration.
"The United States has long considered Taiwan a force for good in the world and a reliable partner," he said in a statement, adding that U.S. support for Taiwan is "bipartisan and unanimous."
The Chinese foreign ministry said on Wednesday hit out at Pompeo's congratulatory statement to Taiwan, saying it "seriously damaged the peace and stability of the Taiwan Strait and China-U.S. relations."
China will take necessary countermeasures and the U.S. will bear the consequences, said the ministry, according to a CNBC translation.