WASHINGTON — 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) marks 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 written in light of last week’s Supreme Court ruling that Hobby Lobby and other closely-held businesses do not have to offer workers some forms of 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 has long pushed President Obama to expand gay rights.

“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.

The American Civil Liberties Union, Lambda Legal and the National Center for Lesbian Rights said in a joint statement that they 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 homosexuals in 2010. House Republicans have said they will not take up the bill, in part because they believe its 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 of Columbia also bar discrimination based on gender identity.

Not all gay rights groups have abandoned ENDA. The Human Rights Campaign continues to support the bill.

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.