Tsai, 59, who took oath today as new President of Taiwan in Taipei, is the head of the Democratic Progressive Party, which advocates Taiwan's independence from the mainland.
"Once again, the people of Taiwan have shown the world through our actions that we, as a free and democratic people, are committed to the defence of our freedom and democracy as a way of life," Tsai said in her address after taking oath.
She called on on both sides to "set aside the baggage of history, and engage in positive dialogue, for the benefit of the people on both sides," the BBC reported.
Experts say what Tsai said in her speech is unlikely to satisfy Beijing. It sees eventual unification with the island as non-negotiable.
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With tensions rising in the South China Sea, Beijing is keen for Taiwan to be its ally rather than be aligned with rival claimants to the disputed islets in the sea.
"Independence is the greatest disaster for the peaceful development of peace in the Taiwan straits and the peaceful development of cross-straits relations," it said.
Commenting on Tsai's swearing in, Foreign Ministry spokesperson Hua Chun Ying said, "I want emphasis that 'One China policy' is widely recognised by the world and one-china principle is important corner stone and prerequisite for China to develop relations with other countries".
"What ever political changes Taiwan may go through, the Chinese government will remain unchanged in sticking to the One-China principle and oppose the Taiwan independence or one China or one Taiwan," Hua said.
"With regard to foreign relations between Taiwan and other countries the one-China policy is a prerequisite and basis for relations China and other counties," she said.
"We have noobjection to Taiwan's unofficial trade relations with other countries. We are opposed to other countries signing official agreements with Taiwan. For any trade arrangements they should be discussed through pragmatic cooperation between the two parts," Hua said.
China and Taiwan split in 1949. But Beijing has always seen the island as a rebel province awaiting reunification.