During a news conference in Montgomery, Riley said he wants a statewide referendum on the amendment held on Nov. 2 this year, at the same time as the presidential election.
Democratic legislators instead support a bill that would hold the vote in 2006.
Riley says voters in Alabama should not be forced to wait two years to decide such an important issue.
Riley says he supports the amendment because he sees marriage as a sacred institution between a man and a woman.
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