Chinese President Xi Jinping speaks at an event marking the 40th anniversary of China's reform and opening up at the Great Hall of the People in Beijing, China December 18, 2018.
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.
Beijing "reserves the option of taking all necessary measures" against outside forces that interfere with peaceful reunification and Taiwanese separatist activities.
Taiwanese President Tsai Ing-wen said on Wednesday that the island's "unification" with China was not possible under the "one country, two systems" model.
Mrs Tsai warned China on Tuesday that Taiwan's people would never give up the kind of freedoms unseen on the authoritarian mainland.
She stressed that Taiwan has been fulfilling its responsibility in maintaining regional stability for the past two years but has in return received threats from Beijing.
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Taiwan is a self-governed democracy and for all practical purposes has acted as an independent nation since 1950, when China's nationalist government was defeated by communist forces and fled there from the mainland.
"That's harming the interests of our Taiwan compatriots", Xi said.
"Peaceful unification and "one country, two systems" are the best methods of realizing unification between the two sides", Xi said as cited by China's official Xinhua News Agency.
President Tsai said she was willing to start a cross-strait political negotiation with China as long as it was organized as an exchange between two sovereign states. In a historic overture, it issued a public letter to the Taiwanese known as the "message to compatriots in Taiwan", calling for an end to military confrontation across the Taiwan Strait and saying it would open communication between the two sides.
When Jiang Zemin took power in Beijing, he largely continued Deng's policies - wooing the island by opening the doors to Taiwan entrepreneurs wanting to set up factories and businesses on the mainland and take advantage of its cheap labour and vast market.
Chinese President Xi Jinping, declaring that independence is not an option for Taiwan, urged both sides to reach an early consensus on unification and not leave the issue for future generations.
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Most Taiwanese say in polls they oppose Xi's goal of unification, and the Communist leadership doesn't recognize the autonomy of Taiwan.
The address was also laced with threats of military force and warnings aimed at the Trump administration, which has shown greater willingness to show support for Taipei by selling arms and dispatching US warships to nearby waters.
Referring to November's local elections in Taiwan, Tsai said that the result was not tantamount to the Taiwanese people surrendering their sovereignty, and that it also doesn't mean that Taipei is ready to make major concessions to Beijing.
The specifics of Mr. Xi's address differed little from what his predecessors have said about Taiwan. Over the past year, Beijing has ramped up efforts to isolate Taiwan, through pressuring global companies and airlines to list the territory as part of mainland China.
A day later on Wednesday, Xi appeared to fire back, saying that China had achieved "a great victory" against Taiwan's pro-independence movement.
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