"Democracy taught us a lesson today, we have to meet the people's higher expectations", Tsai said on Saturday evening.
In a Facebook post, Premier William Lai said he also had offered his resignation to Tsai.
The DPP held on in two of its other strongholds, however, keeping Tainan in the south and Taoyuan in the north.
The DPP is left in control of only six of Taiwan's 22 cities and counties, compared with at least 15 for the Kuomintang.
At a campaign rally Wednesday for her party's Taipei mayoral candidate, Tsai accused China of "intervening" in the elections.
KMT also defeated the ruling party in the central city of Taichung, while Ko Wen-je, the independent mayor of the capital, Taipei, appeared on track to win a second term.
In the run-up to the election, Tsai and her government have repeatedly said China is attempting to sway election results with its "political bullying" and "fake news", accusations Beijing denies.
A spokesperson for the US State Department praised Taiwan for "demonstrating the strength of their vibrant democratic system through a successful round of elections".
Voters line up to cast their ballots in Taipei on Saturday.
The CEC is expected to announce the official results of all local elections at 11 p.m.Читайте также: Wizards Willing To Trade John Wall, Bradley Beal
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.
Tsai's domestic reform initiatives, from the island's pension scheme to labor law, have also come under intense voter scrutiny recently.
Confidence in the Government has waned in recent months after reform moves upset both the opposition and some supporters, who said Ms Tsai had backed away from promises to reduce the deficit and cut pollution.
The 10 referendum proposals involved a wide range of issues, including whether to legalize same-sex marriage, whether to reduce thermal power plant production to curb air pollution, whether to ban food imports from radioactive contaminated areas in Japan, and whether to use "Taiwan" as the name to participate in global sporting events such as the 2020 Tokyo Olympics.
"This is a small step for myself, but a big step for mankind", said Chi Chia-wei, a veteran gay rights activist who had petitioned Taiwan's Constitutional Court to take up the issue.
Taiwan's top court legalised gay marriage in May 2017 and ruled that it must be brought in within two years.
Taiwanese have begun voting in midterm local elections seen as a referendum on the administration of President Tsai Ing-wen, amid growing pressure from the island's powerful rival China.
Conservative groups asked whether the legislation - defining marriage as a union between a man and a woman in Taiwan's Civil Code - should remain unchanged, while LGBT activists demanded equal marriage rights.
Jennifer Lu, a spokeswoman for Marriage Equality Coalition Taiwan, said they were saddened by what she described as the "absurd referendums" and blamed government "incompetence" for allowing the anti-gay marriage votes to go ahead.При любом использовании материалов сайта и дочерних проектов, гиперссылка на обязательна.
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