Voters in 11 US states have overwhelmingly rejected gay marriages, in referendums being held on the issue.
Gay marriages took place in San Francisco this year
Oklahoma, Georgia, North Dakota, Ohio, Kentucky, Michigan, Montana, Utah, Mississippi and Arkansas backed constitutional amendments limiting marriage to a union between a man and a woman.
Oregon, which had been expected to reject the proposed ban, was backing a similar amendment by a smaller margin.
Ohio is reported to have also backed an amendment against civil unions for gay couples.
George W Bush has said he is seeking to change the US constitution to specify that marriage can only take place between a man and a woman.
"As we profess tolerance... we shouldn't change - or have to change - our basic views on the sanctity of marriage," he said in the third presidential debate.
Democratic candidate John Kerry had responded by referring to Vice-President Dick Cheney's daughter who is openly gay and who works on the Republican election team.
"I think if you were to talk to [Vice-President] Dick Cheney's daughter, who is a lesbian, she would tell you that she's being who she was, she's being who she was born as," Mr Kerry said.
He was heavily criticised by the American media for bringing up the sexuality of Mr Cheney's daughter in his campaign.
Not everyone is in favour of single-sex marriages
Mr Cheney's views appear to fly directly in the face of President Bush.
He has said people ought to be free to enter into any kind of relationship they wanted.
He also said individual states, and not Washington, should be allowed to rule on the issue of homosexual marriage.
San Francisco, in California, became the first place in the US earlier this year where gay couples were able marry.
But California's Supreme Court in August annulled about 4,000 gay marriages that took place in the city.
Missouri in the summer voted overwhelmingly to ban gay marriage.
Gay marriage is still a hugely controversial subject across the country.
Observers have said the issue is likely to have brought voters to the polls, which they say could be to the Republicans' advantage.