Opposition to same-sex marriage crested after the court ruling.
A woman casts her ballots at a polling station during local elections and referendum on same-sex marriage, in Kaohsiung, Taiwan.
Yesterday, Mr Ma Xiaoguang added that China wants to enhance exchanges and cooperation between Taiwan's counties and cities and their mainland counterparts, but "on the basis of correct understanding of the nature of cross-strait relations".
Ting Shou-chung said on Sunday he was disputing the results, which gave a narrow victory to incumbent mayor Ko Wen-je, an independent.
Now, the independence-leaning party controls only six of Taiwan's cities and counties, while the Beijing-friendly Kuomintang party controls 15.
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.
Such was the case for KMT mayoral candidate Han Kuo-yu, who took DPP stronghold Kaohsiung, he told Guancha.cn, a news portal.
Candidates fanned out across the island to shake hands and canvass votes, and held noisy, colourful rallies that have become the hallmarks of Taiwan's vibrant democracy, in marked contrast to China where the Communist Party tolerates no dissent to its rule.
In Asia's first such ruling, Taiwan's Constitutional Court declared in May last year same-sex couples had the right to legally marry, and set a two-year deadline for legalisation.
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In practice, that would bar most asylum seekers who entered Mexico from filing asylum claims in the United States. Gastélum said on Friday that he'd asked the United Nations for aid to help with the influx of asylum seekers.
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.
Ms Tsai's domestic reform initiatives, from the island's pension scheme to labour law, have also come under intense voter scrutiny recently.
Tsai has made little progress despite campaigning on a promise of marriage equality in the run-up to elections in 2016.
Confidence in the government has waned in recent months after reform moves upset both the opposition and some supporters, who said Tsai had backed away from promises to reduce the deficit and cut pollution.
Voters on Saturday also cast ballots on 10 referendums, including one on whether to amend the civil code to include same-sex marriage - which was legalized a year ago - and on whether to uphold a commitment to ban nuclear energy by 2025.
On the side of equality was the "grassroots campaign unlike anything Taiwan has seen before", comprised of LGBT+ activists and allies.
What do you think of Taiwan's rejection of gay marriage in today's referendum?
Meanwhile other organisations welcomed the result.
The spokesman also said the defeat of a referendum proposition that the island should seek to compete in the 2020 Olympics as Taiwan, rather than Chinese Taipei, showed that putting Taiwanese athletes' interests at stake "was against the will of the people".
Although the International Olympic Committee has already ruled out any changes and warned that Taiwan could even lose its accreditation, many see the vote as a test of support for independence and a means to fire up the DPP base. Beijing, which has never given up its claim to Taiwan, denies the allegations.