WASHINGTON — The U.S. Census Bureau on Tuesday sharply revised downward its estimate of the number of same-sex households across the country, reflecting confusion over how to accurately count gay and lesbian couples that have gained varying degrees of legal recognition of their partnerships over the past decade.

Unlike with factors such as race, gender and household income, the Census Bureau doesn’t attempt to count gay, lesbian, bisexual and transgender individuals. Only in the 2000 census did it start to count same-sex households, and demographers say the wording of the forms may have led to an unusually high number of inaccurate responses.

The bureau said there were approximately 646,000 same-sex households in the United States in 2010. It originally counted more than 900,000 same-sex households in 2010, but then estimated that as much as 28 percent of that count was actually opposite-sex.

“I applaud the bureau for trying to provide the most accurate information,” said Gary Gates, a demographer at the University of California-Los Angeles who specializes in the gay and lesbian population and reviewed the Census Bureau’s revisions. “The problem is, people can make mistakes.”

In spite of the downward revision, Gates said the census might have actually undercounted same-sex couples.

“I’ve been one of the voices saying to the bureau that ‘the way you’re measuring has serious problems,’” he said.

He suggested changing the wording from husband/wife or unmarried partner, combined with sex variables, that the form currently uses. He suggested using the simpler categories used in Canada and Great Britain for couples: Opposite-sex husband/wife, Same-sex husband/wife.

“It’s a way to get much more accuracy,” Gates said. “Unless they do that, they’re never going to fix this problem.”

But, he said, there could be political problems with that wording because of the Defense of Marriage Act, which prohibits federal recognition of same-sex marriages, though it doesn’t prevent individual states from recognizing them.

The Obama administration stopped defending the Defense of Marriage Act earlier this year and called for its repeal, prompting Republican leaders in the House of Representatives to mount their own defense of the law, passed by Congress and signed by President Bill Clinton in 1996.

Gay and lesbian couples have seen tremendous changes since the 2000 census, which counted about 358,000 same-sex households. The U.S. Supreme Court overturned the remaining state laws that criminalized same-sex activity; gay couples gained marriage rights or marriage-like rights in several states; and just last week, the U.S. military ended its longstanding prohibition on openly gay service members.

Public opinion has shifted. An Associated Press and National Constitution Center poll recently showed that 53 percent of Americans supported giving marriage rights to same-sex couples, with 47 percent opposed. A higher number, 57 percent, supported giving the same government benefits to same-sex married couples as opposite-sex ones.

Evan Wolfson, the founder and president of Freedom to Marry, a group that’s been working toward full marriage rights for gays and lesbians in all 50 states, said the “imperfect information” released by the census shows that there are gay couples in every corner of the country and points to the need to repeal the Defense of Marriage Act.

“We live in families. We are starting to have legal respect for those families, and many of us are getting married,” he said. “The sooner the law stops treating these families unequally, the better.”