With gay marriage being debated by the United States Supreme Court, some of the major backers of efforts to legalize it around the country are casting their attention to the next fight: anti-discrimination bills in a variety of states.

The new effort, Freedom for All Americans — a $5 million-a-year campaign over the next five years — is predicated on the fights around gay marriage, which played out state by state until reaching the Supreme Court in a fight that, advocates hope, will legalize same-sex marriage nationally.

The idea behind FFAA is to eventually get a major federal nondiscrimination bill that protects people from prejudice based on sexuality and gender identity. In the meantime, the group’s backers will fight on a state-by-state level, such as in Indiana, where opponents of Gov. Mike Pence’s religious rights bill worked to force a revision that added gay rights protections.

The new group is a partnership of the American Unity Fund, a super PAC created by the hedge fund executive Paul Singer, as well as the Gill Foundation and the Gill Action Fund. Tim Gill, a Colorado-based Democratic activist and philanthropist, has been a major financial backer of same-sex marriage efforts.

And Mr. Singer and another hedge fund executive, Dan Loeb, were among the financial backers of the efforts in New York, along with then-New York City Mayor Michael R. Bloomberg and Gov. Andrew M. Cuomo, to pass a gay marriage law in 2011.

“We think this needs to be legislated at both a state and federal level, so we’re approaching it from both standpoints,” Mr. Loeb said in a rare interview about his efforts. “There are too many states that don’t have employee non-discrimination acts.”

The news was first reported by Bloomberg Business Week.

Mr. Loeb said that the effort, which is bipartisan in nature, is critical toward changing understanding against gays. He also suggested that appeals on the issue toward Republicans will be crucial.

“It never works if you bully, or cajole – you have to articulate why” someone should be in favor of efforts such as the anti-discrimination bills, he said, suggesting it “should be a pretty easy position to take” for many lawmakers, no matter how conservative they are.

“There are a number of legislators, who because of their religious beliefs” can’t back gay marriage, he said. That is less of an issue with discrimination laws, he said.

“I think it’s political suicide in a general election” for the Republicans not to support such efforts, he said. “They’ve got to figure out a way to get through the primaries and make a case for something that the primary base is not there yet” and sold on, he said.

Mr. Gill, in an emailed statement, said that having Republicans backing the effor is vital, just as it was in the debate over same-sex marriage.

“We’re not going to win equality in states like Indiana or Georgia without the support of conservative business leaders like Dan Loeb,” he said. “Having allies like Dan sends a clear message that the tide of support for fairness and opportunity won’t be stopped.”

According to Matthew McTighe, who is running the FFA campaign, some 33 states don’t have comprehensive laws protecting gay, lesbian and transgender rights. The group will focus on making existing anti-discrimination laws in states like New Hampshire more comprehensive than they are now to, for instance, give explicit protection for transgendered people.

Those behind the effort plan to ramp up the drive as the 2016 election campaign gets heats up. And they have already been focusing on fighting religious rights bills in places like Georgia and North Carolina.

Mr. Loeb said that the push has already borne fruit in at least one case with the 2016 presidential field: Jeb Bush, the former Republican governor of Florida, who firmly backed the Indiana bill but later said he supported the anti-discrimination protections that were added.

“I think in Jeb’s case he kind of came around and saw the light,” Mr. Loeb said. “He kind of jumped the gun on that. I think it’s important that supporters of these candidates communicate with them consistently, talk to them about this, and make clear that it’s an important issue — it’s not going to go away.”