Several major gay rights groups withdrew support Tuesday for legislation that would bolster gay and transgender rights in the workplace, saying they fear that private companies will use a recent Supreme Court ruling to claim religious exemptions from the bill.

The calls to rewrite the ­Employment Non-Discrimination Act (ENDA) mark a major setback for the White House, which had used Senate passage of the legislation last fall as a way to draw a contrast with House Republicans, who have refused to vote on the measure.

The groups said they can no longer back ENDA as currently written in light of a decision last week by the Supreme Court, which ruled that Hobby Lobby and other closely held businesses do not have to offer their employees contraceptive coverage if it conflicts with the owners’ religious beliefs.

Signs of crumbling support for ENDA came first Tuesday from the National Gay and Lesbian Task Force, one of several gay rights groups that pushed Obama to expand gay rights since the start of his presidency.

“If a private company can take its own religious beliefs and say you can’t have access to certain health care, it’s a hop, skip and a jump to an interpretation that a private company could have religious beliefs that LGBT people are not equal or somehow go against their beliefs and therefore fire them,” said Rea Carey, the group’s executive director.

A coalition led by the American Civil Liberties Union, Lambda Legal and the National Center for Lesbian Rights said in a joint statement Tuesday that it also would be withdrawing support.

The Senate approved ENDA with bipartisan support last November, marking the first time federal lawmakers had approved legislation to advance gay rights since repealing the military’s ban on openly gay men and women in uniform in late 2010. House Republicans have said they will not take up the bill, in part because they believe the bill’s current religious exemptions aren’t clear or broad enough.

Twenty-one states and the District of Columbia have laws prohibiting workplace discrimination based on sexual orientation, while 17 states and the District also bar discrimination based on gender identity. Hundreds of the nation’s largest companies have similar bans.

Not all gay rights groups have abandoned ENDA. The Human Rights Campaign said Tuesday that it continues to support the bill “because it will provide essential workplace protections to millions of LGBT people.”

On another front, Carey’s group also is pushing against a broad religious exemption in an executive order that Obama is expected to sign banning discrimination against gay, lesbian and transgender employees of federal contractors. Gay rights groups say the order is the last significant action that Obama is likely to take in expanding gay rights without the cooperation of Congress.

But religious leaders, responding to last week’s contraception ruling, have redoubled efforts to ensure that Obama includes a religious exemption in his executive order.

Sen. Tammy Baldwin (D-Wis.), a lead sponsor of ENDA and the Senate’s first openly lesbian member, said Tuesday that she was still reviewing the decision by gay rights groups to withdraw support for the bill. Baldwin said the bill’s religious exemption language had been tweaked last year in order to secure more support from Democrats and Republicans.

Among gay rights groups, Baldwin said, “there was clearly discomfort expressed at that point.”