Xi was speaking on the anniversary of the "Message to Compatriots in Taiwan" on January 1, 1979, when China declared an end to what had been routine artillery bombardment of Taiwan-controlled offshore islands and offered to open up communication between the two sides.
Xi's words that Taiwan "must and will be reunited" follow along with Beijing's long-standing view on its most sensitive issue, though there is some worry in Taiwan that with his increased power Xi is in a stronger position than his predecessors when it comes to achieving this goal.
President Xi thundered against past efforts in Taiwan to become legally independent of China and said the two sides should pursue a "one country-two systems" model of unification that his government applied to Hong Kong in 1997.
Tsai's Democratic Progressive Party (DPP) does not accept the 1992 Consensus - a diplomatic agreement made between Taiwan and China acknowledging the existence of "one China".
"The differences in [both sides' political] systems is not an impediment to unification, nor should it be an excuse for separation", Xi said, adding that the implementation of the "one country, two systems" framework to Taiwan would consider the nation's situation and suggestions from various sectors of society on both sides of the Taiwan Strait.
The "Message of Compatriots in Taiwan" on January 1, 1979, declared an end to routine artillery bombardment of Taiwan-controlled islands close to China, marking a turning point from decades of hostility between the two sides.
Xi did tout Taiwan's "great victory in frustrating the Taiwan independence movement and other separatist activities" - one day after Tsai said Taiwan's "greatest challenge" was combating Beijing's attempts to "interfere in Taiwan's internal politics and social development".
"Nobody, and no party, can change the historical and legal that Taiwan is part of China and that both sides of the strait belong to China", Xi said in Beijing.More news: Suspect arrested in shooting death of California officer
China still sees Taiwan as part of its territory to be reunified, despite the two sides being ruled separately since the end of a civil war on the mainland in 1949.
Tsai instead stressed the need for China to accept Taiwan's democratic values and the "fundamental differences" between the two societies, saying on Tuesday that cross-strait ties "cannot depend on vague political preconditions or forced submission to "passwords" or acceptable phrases".
Taiwan President Tsai Ing-wen holding a news conference in reaction to Chinese President Xi Jinping's speech in Taipei.
After the election of Tsai in 2016, Beijing actively sought to discourage mainland Chinese from visiting the island, resulting in just 2.3 million mainlanders visiting Taiwan in 2018, down from 2.7 million in 2017, and 3.5 million in 2016.
In 2018, the USA sent multiple ships through the Taiwan Strait - which China considers its territory but the United States and others see as worldwide waters open to all - infuriating Beijing.
But Xi's vision of unification with China has little support within Taiwan.
All people in Taiwan must "clearly recognise that Taiwan independence would only bring profound disaster to Taiwan", Xi said.
Washington also remains Taipei's most powerful unofficial ally and its main arms supplier despite switching diplomatic recognition to Beijing in 1979.