Tsai took office as the island's first female president after winning a landslide victory in January to defeat the ruling Kuomintang, ending an eight-year rapprochement with Beijing under outgoing president Ma Ying-jeou.
Voters felt Ma had moved too close to China, which still sees self-ruling Taiwan as part of its territory awaiting reunification.
Beijing-sceptic Tsai swept in with a campaign to restore Taiwanese pride, a message that resonated with a public tired of living in China's shadow.
"The two governing parties across the strait must set aside the baggage of history, and engage in positive dialogue, for the benefit of the people on both sides," she said.
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Relations with Beijing have already cooled since she won the presidency with China putting growing pressure on Tsai to back its "one China" message - the bedrock of the thaw under outgoing leader Ma Ying-jeou.
Tsai and her Democratic Progressive Party have never recognised the concept.
"Cross-strait relations have become an integral part of building regional peace and collective security," she said.
"In this process, Taiwan will be a 'staunch guardian of peace' that actively participates and is never absent."
However, she still emphasised the need for Taiwan to diversify the economy and end its over-reliance on the mainland for trade.
She also expressed the island's commitment to its vibrant democratic culture.
"We, as a free and democratic people, are committed to the defence of our freedom and democracy as a way of life...My dear fellow Taiwanese, we did it," she said.
In an editorial, the Global Times - a newspaper owned by the People's Daily group that often takes a nationalistic tone - said Tsai's assumption of power heralded "a new era for a cross-Straits region that is characterised by uncertainty".