Beijing defends the idea of "one country, two systems" for Taiwan, as it does with Hong Kong.
"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's inauguration speech repeated her election campaign pledge that her government would only deal with China on an equal footing, and would continue to insist on its freedom, democracy and sovereignty in the face of threats of invasion - which Beijing refers to as "reunification".
China said it was willing to "create a vast space for peaceful reunification", but will "not leave any room for all forms of Taiwanese independence separatist activities".
The US recognised the People's Republic as the "sole legal government of China", while "acknowledging" Beijing's position that Taiwan is part of China.
Beijing's proposal has been overwhelmingly rejected in Taiwan.
While Taiwan dropped its bid on Monday to participate as an observer at the World Health Assembly due to opposition from Beijing and other China-friendly members, its dedication to providing proactive assistance to other countries suffering COVID-19 outbreaks has coalesced with Tsai's stewardship of a bolder Taiwan that seeks to assert itself as a nation, outside the sphere of cross-strait affairs.
She said China's moves to downgrade Taiwan and undermine the status quo of the Taiwan Strait, under its "one country, two systems" principle, is unacceptable.
China denounced a rare message from Secretary of State Michael Pompeo to Taiwan's President as "wrong and very dangerous", as tensions between the two sides flared anew over U.S. overtures toward the democratically ruled island.
He continued, saying, "I think we are at a turning point and there may be significant progress in U.S. -Taiwan relations". She added that she looks forward to furthering the friendship based on their many shared values and interests.
China considers Taiwan, where the mainland's defeated nationalists fled in 1949, to be a province awaiting reunification - by force if necessary - and has sought to exclude it from global organizations.
Taiwanese authorities had been allowed to participate in the World Health Organization under the name "Chinese Taipei" from 2009 to 2017, but the World Health Organization claimed that it has "no mandate" to invite Taiwan to its assembly, as it is not recognized as a state by the United Nations.
"China urges the U.S. side to immediately correct its mistakes", the ministry said in a statement posted on its website Wednesday.
"It is very apparent that Tsai will continue her pro-U".
On Wednesday May 20th, the Chinese mainland spokesperson Ma Xiaoguang recommended the United States to value the basic norms of worldwide relations, and discontinue any form of official exchanges with the Taiwan region. According to Taiwan's Ministry of Foreign Affairs, this also marks the first time in history that a sitting USA secretary of state sent well wishes for Taiwan's presidential inauguration.
A separate video message from Ms. Lekhi was also played at the inaugural, in which she wished Ms. Tsai "great success and the continued strengthening of the comprehensive relations between India and Taiwan".