A solid majority of Australians 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 took part in the survey, 61.6 percent voted yes and 38.4 percent voted no, officials announced on Wednesday morning. Participation was high, with 79.5 percent of voting-age Australians taking part.

“The Australian people have spoken, and they have voted overwhelmingly ‘yes’ for marriage equality,” said Prime Minister Malcolm Turnbull, who had called the national survey as a way to put pressure on conservative lawmakers, many from his own party. “They voted ‘yes’ for fairness, they voted ‘yes’ for commitment, they voted ‘yes’ for love.”

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, at Prince Alfred Park in Sydney, broke into cheers as the news became clear.

“This is our proudest moment as gay and lesbian Australians,” said Chris Lewis, 60, an artist from Sydney, who waved a large rainbow flag he bought in San Francisco about 30 years ago. “Finally I can be proud of my country.”

Annika Lowry, 42, who brought her four-year-old daughter to the celebration, said the vote “was not just about us — it’s for our kids, so that they know equality is important.”

Alex Greenwich, a state lawmaker from New South Wales and the co-chairman of Australian Marriage Equality, an advocacy group, said the vote “ 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.”

In calling for the national survey, Mr. Turnbull sought public backing for a shift in social policy that was opposed by many members of his center-right Liberal Party.

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.