MELBOURNE, Australia — Australians have voted in favor of same-sex marriage in a historic survey that, while not binding, paves the way for Parliament to legally recognize the unions of gay and lesbian couples.

Of 12.7 million Australians who voted in the survey, 61.6 percent voted yes and 38.4 percent voted no, officials announced on Wednesday morning.

The results were announced as proponents of gay rights gathered at public events in cities around the country to watch the news. The largest crowd, Prince Alfred Park in Sydney, broke into cheers as the news became clear.

“It shows that Australians have truly come together in support of their gay and lesbian mates and have said that everybody should be able to have the freedom to marry,” said Alex Greenwich, a state lawmaker from New South Wales and the co-chairman of Australian Marriage Equality, an advocacy group.

In calling for the national survey, Prime Minister Malcolm Turnbull sought public backing for a shift in social policy that many members of his Conservative Party oppose.

Mr. Turnbull voted yes, and urged other Australians to do so as a matter of fairness, seeking to blunt opposition from far-right members of his party.

Dean Smith, a federal senator from the right-leaning Liberal Party, who is gay, said that as a result of the survey, he would immediately introduce a bill to legalize same-sex marriage. He said on Tuesday that he believed he had the votes to pass the legislation in the Senate and send it to Parliament’s lower house for approval.

Lyle Shelton, a Christian lobbyist who was the “no” campaign’s most outspoken advocate, said he would begrudgingly “accept the democratic decision.”

“Millions of Australians will always believe the truth about marriage, that it’s between one man and one woman,” Mr. Shelton said. “It could take years, if not decades, to win that back.”

In 2015, Ireland was the first country to legalize same-sex marriage by referendum, but the same year, voters in Slovenia rejected a law legalizing such unions.

In the United States, Maine, Maryland and Washington became the first states to legalize same-sex marriage by referendum, in 2012; the country’s Supreme Court legalized same-sex marriage across the nation in 2015.

The survey in Australia was controversial, not only because it put such a thorny issue before the whims of direct democracy but also because of its cost.

The survey, a comprehensive — but expensive — opinion poll, was contentious from its conception. As the deadline approached for citizens to mail in their ballots, passions were inflamed by heartfelt pleas and vitriolic attacks.

Many advocates for same-sex marriage opposed the survey, saying that human rights should not be a matter for an up-or-down vote and urging Parliament decide the matter.

Estimates put the cost of the survey around 122 million Australian dollars, or $97 million. The poll was not a legally required step for changing the law.

Activists in September challenged the survey’s legality in Australia’s High Court, arguing that it was an unconstitutional use of tax money, but the court allowed the poll to proceed.

The results on Wednesday results make the country’s path to same-sex marriage much clearer.

Mr. Greenwich said the outcome delivered “an unequivocal mandate for Parliament to legislate for this bill as soon as possible for a fair bill this year.”

Focus has already shifted to that bill, and what form it will take.

“After a cost of 122 million, and over two months of campaigning and years of public discussion, it makes no sense to delay a parliamentary debate,” Mr. Smith, the Liberal senator, said in an interview. “Australians upheld their end of the bargain by voting en masse. Now it’s time for Parliament to uphold its end of the same deal.”

Mr. Smith’s bill provides for some religious protections and allows members of the clergy to refuse to solemnize marriages that conflict with their religious beliefs.

“That bill is obviously manifestly inadequate,” said Mr. Shelton, the Christian lobbyist, who added that it focused on wedding ceremonies. “The ‘yes’ side should make good on its promise that no one else’s freedoms would be affected. They’ve maintained this all along. They’ve said that our concerns about freedom of speech and freedom of religion are red herrings.”

Mr. Shelton said Mr. Smith’s bill would affect Muslim and Christian schools who wish to teach that marriage is between one man and one woman. “We’re worried about bakers and florists being taken to court, as has occurred in the United States,” he added.

An alternative bill, proposed by another Liberal Party senator, James Paterson, has more robust religious protections. His bill would allow service providers like bakers and photographers to refuse service to same-sex couples, without facing legal action. His bill would provide additional anti-discrimination protections for religious people and businesses opposed to gay marriage. Reflecting the national debate that often centered on the well-being of children, Mr. Paterson’s bill would allow parents the right to take their children out of classes that “conflict with their values.”

Mr. Turnbull, who voted “yes,” said he did not believe Mr. Paterson’s bill could pass Parliament. “I don’t believe Australians would welcome, and certainly the government would not countenance, making legal discrimination that is illegal, that is unlawful, today.”

At least seven members of Australia’s Parliament have publicly committed to voting against any bill to legalize same-sex marriage, according to a report from the Australian Broadcasting Corporation. Most lawmakers, however, said they would support such a bill.

“There’s no denying that this has been tough for many people. This has been a campaign which has gone on for more than 10 years,” said Mr. Greenwich, the same-sex marriage advocate. “This result is a reflection of the leadership that’s been shown by everyday Australians during this campaign. It shows that Australians truly did have the opportunity to shape our nation as a fairer and more equal place.”

Isabella Kwai contributed reporting from Sydney, Australia.

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