Tsai won a second term over the weekend with a record 8.2 million votes, an outcome that was seen as a forceful rebuke of China's ongoing campaign to isolate the self-ruled island.
China's leadership had made no secret of its desire to see Tsai turfed out because she and her party refuse to acknowledge their view that the island is part of a "one China".
Beijing regards Taiwan as its territory and has vowed to one day seize it, by force if necessary -- especially if it declares independence.
But in her first interview since Saturday's re-election, Tsai told the BBC there was no need to formally announce independence because the island already runs itself.
"We don't have a need to declare ourselves an independent state," she said in the interview, which aired on Wednesday.
"We are an independent country already and we call ourselves the Republic of China, Taiwan."
Modern Taiwan has been run separately from the mainland for the last 70 years.
For decades, it was a dictatorship under Chiang Kai-shek's nationalists following their 1949 defeat to the communists in China's civil war.
But since the 1980s, it has morphed into one of Asia's most progressive democracies, although it is only diplomatically recognised by a dwindling handful of countries.
Polls show growing numbers of Taiwanese reject the idea that the island should be part of the Chinese mainland.
"We have a separate identity and we're a country of our own," Tsai said. "We deserve respect from China".
'Stink for eternity'
China has greeted Tsai's re-election with anger, warning against any move to push the island closer towards independence.
"Splitting the country is doomed to leave a name that will stink for eternity," Foreign Minister Wang Yi said this week.
Chinese state media also accused Tsai of winning the election through cheating, without providing evidence.
On Wednesday, Beijing's Taiwan Affairs Office said there were no plans to change policy towards the island after the landslide election.
"Taiwan's future lies in the unification of the country," spokesman Ma Xiaoguang said, adding its future must be decided by "all Chinese people".
But Tsai said China should respect the wishes of Taiwan's electorate.
"I hope the Chinese side can understand in-depth the opinion and will expressed by Taiwanese people in this election and can review some of their current policies," she told reporters on Wednesday.
Tsai was speaking as she announced a new "anti-infiltration law" had been signed into effect making it illegal to launch political activities that are backed or funded by "hostile external forces".
Supporters say the bill is aimed at clamping down on China's infiltration of Taiwan's politics while opponents called it anti-democratic.
Costs of war
In her BBC interview -- which came as Taiwan held annual military drills on the south of the island -- Tsai warned Beijing against sending in troops.
"Invading Taiwan is something that is going to be very costly for China," she said.
Critics accuse Tsai of being needlessly antagonistic towards Beijing.
But Tsai said she had resisted pressure from within her own party to be more forceful on the issue of independence.
"There are so many pressures, so much pressure here that we should go further," she said.
"Maintaining a status quo remains our policy... I think that is a very friendly gesture to China."
Tsai has repeatedly said she is willing to talk to Beijing as long as there are no pre-conditions.
But Beijing has refused, cutting off official communication with her administration.
Over the last four years, it has also has ramped up economic, military and diplomatic pressure, hoping it would scare voters into supporting the opposition.
But the strong-arm tactics backfired with voters resoundingly backing Tsai for another four more years.