Tsai and officials from her ruling Democratic Progressive Party (DPP) have repeatedly said they believe China has meddled in the lead-up to the elections through a "fake news" campaign, which Beijing has denied.
China claims sovereignty over self-ruled Taiwan, causing decades of friction between the two sides.
However, a spokesman on Sunday was quick to cite the election results as evidence that Taiwanese were becoming fed up with Tsai's approach.
She said she would not accept the resignation of her premier William Lai, who had offered to quit earlier in the evening.
Chiu Chui-cheng, deputy minister of Taiwan's Mainland Affairs Council, told Reuters the government had always welcomed exchanges with China, but Beijing's "political preconditions" had hindered such contacts. "The elections are not just local, they're about governing style", Jung said.
Activists are mobilizing first-time voters for the gay marriage rights measures because "a lot of younger people understand the idea of gender equality", said Chang Ming-hsu, project manager with the Taipei-based advocacy group Gender Equity Education Coalition.
"The Taiwan election once again demonstrated what is democracy". Government employees who feel slighted by pension cuts that took effect in July probably mobilized against Tsai's party, Jung said.
A Chinese spokesman was quoted by the Xinhua news agency as saying the results "reflected the strong will of the Taiwanese public in sharing the benefits of the peaceful development across the Taiwan Strait, and desires to improve the island's economy and people's wellbeing".
Beijing has intensified pressure on Taiwan under Tsai, upping military drills, poaching diplomatic allies and successfully convincing worldwide businesses to list the island as part of China on their websites.
Observers in Taiwan pointed out that the KMT's wins should not be read as tantamount for a win for reunification with China, as unlike presidential races, a candidate's stance on cross-strait ties may take a back seat in regional elections, where debates normally center around economic and livelihood issues.
By most economic metrics, Tsai hasn't performed badly as president. Hebe said "We still work hard and please keep going!" "It doesn't have to be the 1992 Consensus".
The Nationalists had campaigned on a pro-business platform, while also advocating a more conciliatory line toward Beijing.
In Taipei, Ko Wen-jo, an independent candidate, won reelection, defeating both KMT and DPP candidates. "Any win by a political party is a win for democracy", Chen said.
The majority of voters approved a measure Saturday stating "Civil Code regulations should restrict marriage to being between a man and a woman" and two other measures opposing same-sex marriage while rejecting measures to legalize same sex marriage and asking if civil code marriage regulations "should be used to guarantee the rights of same-sex couples to get married".
But the authorities are expected to pass a special law for same-sex unions after the vote.
However, campaigners fear the eventual legislation will be weaker.
"They usually do not illustrate any concrete examples about why they are against (same-sex marriage) and they usually make up some facts like once the laws pass, you can not call your father papa, you can not call your mother mama", Shiau said. Legislators, though mindful of public opinion, are obligated to carry out the legal order.