Massachusetts Gov. Mitt Romney (search) says babies born to couples of the same sex should be given amended birth certificates, but supporters of gay marriage who want to change those certificates say the governor's formula for doing so is wrong.

Click in the box to the right to watch a report by FOX News' Alisyn Camerota.

Birth certificates (search) are supposed to establish identity and parentage. In Massachusetts, the only state in the union where same-sex marriage (search) is legal, gay rights advocates want the words "Mother" and "Father" removed from birth certificates, and put in their place the terms "Parent A" and "Parent B."

"There should be no doubt in Massachusetts that Massachusetts records should accurately reflect the true nature of Massachusetts families and that includes same-sex couples," said Michele Granda, staff attorney for Gay and Lesbian Advocates and Defenders.

Romney has instructed hospitals to cross out the words "Mother" or "Father" and write in the phrase "Second Parent."

"I'm opposed to taking the Massachusetts birth certificate and removing the term 'Mother' and 'Father' and substituting 'Parent A' and 'Parent B,'" Romney said. "Look, each child has a mother and a father. They should have the right to have that mother and father known to them and that's something I'd like to preserve on a birth certificate."

Romney opposes same-sex marriage. Gay advocates say his latest stand is discriminatory.

"There's no need for the governor to be stigmatizing the children born to same-sex couples just because he does not personally approve of same-sex couples," Granda said.

As Romney contemplates a run for president, the Republican governor from a liberal Northeast state knows his position on birth certificates has to appeal to Southern and Midwestern conservatives. Still, Romney said, he's voicing his conscience.

"My view is that that's wrong on paper and it's wrong on fact. Every child deserves to have a mother and a father, and a birth certificate should reflect mothers and fathers," he said.

Like the decision allowing gay marriage in Massachusetts, the description of a parent on birth certificates also appears to be destined for the court.