Tsai said in her socially distanced speech at the Taipei Guest House that she was willing to engage in dialogue with China.
For decades, Taiwan's leaders - and many voters - saw themselves as the true representatives for all of China, even as the vast majority of nations switched diplomatic recognition to Beijing.
Taiwan, which has its own currency, flag, army, diplomacy and government, has in fact been politically separated from China for 70 years.
Both sides have an obligation to find a way to coexist in the long term and prevent the intensification of antagonism and differences, "said the president, a supporter of Taiwanese independence".
Taiwan President Tsai Ing-wen.
Beijing urges Washington to "stop interfering in China's internal affairs and stop any words and deeds that would harm the peace and stability of the Taiwan Strait and Sino-U.S. relations", the ministry said.
Tsai renewed her offer of talks with Beijing.
With eyes on more participation at global level, Tsai said: "Over the next four years, we will continue to fight for our participation in worldwide organizations, strengthen mutually beneficial cooperation with our allies, and bolster ties with the US, Japan, Europe, and other like-minded countries". "I know that no matter the challenges we may face, we will stand together in freedom, democracy, and solidarity", she said.
Several senior U.S. officials and Senators sent messages of congratulation, including Secretary of State Mike Pompeo, the presumptive Democratic Presidential candidate Joe Biden, Senior Director of the U.S. National Security Council Mike Pottinger, and Assistant Secretary of State for East Asian and Pacific Affairs David Stilwell.
China's foreign ministry Wednesday said U.S. Secretary of State Mike Pompeo has done serious damage to U.S. She said the Taiwan-US relationship is strong and full of promise.
Mr Pompeo referred to Taiwan as a "force for good in the world and a reliable partner", sentiments echoed in statements by presumptive Democratic presidential nominee Joe Biden and several U.S. members of congress.
Tsai famous the quantity of consideration Taiwan had acquired over current months, and thanked residents for his or her efforts in responding to the outbreak.
China has stepped up its military drills near Taiwan since Tsai's re-election, flying fighter jets into the island's air space and sailing warships around Taiwan.
The sides split amid civil war in 1949 and Beijing has cut off ties with Ms Tsai's government over her refusal to accept its demand that she recognise the island as a part of China.
For this reason, "for the short term, I think China will continue to exert pressure and try to intimidate Taiwan and to deter the United States", Bosco said.
Along with Su, most cabinet members remained in their posts, including Foreign Minister Joseph Wu and Chen Shih-chung, the health minister who also helms Taiwan's epidemic command center and has been instrumental in the country's success in combating the coronavirus.
He explained: "We should increase the number of both naval operations and air operations through the Taiwan Strait".