PORTLAND, Maine — Maine voters repealed a state law Tuesday that would have allowed same-sex couples to wed, dealing the gay rights movement a heartbreaking defeat in New England, the corner of the country most supportive of gay marriage.

Gay marriage has now lost in every single state — 31 in all — in which it has been put to a popular vote. Gay-rights activists had hoped to buck that trend in Maine — known for its moderate, independent-minded electorate — and mounted an energetic, well-financed campaign.