Republican lawmakers in Indiana promised Monday to amend a religious liberties bill that critics have labeled as anti-gay, bowing to protests that have rapidly spread to several other states considering similar measures.

Indiana House Speaker Brian Bosma (R) said the legislature would act as soon as this week to “clarify” the state’s new Religious Freedom Restoration Act, which grants individuals and businesses legal grounds to defend themselves against claims of discrimination. The fix, Bosma said, would make clear that the law does not allow people to discriminate against gays, as critics contend.

Opponents of the measure say the fix suggested by Bosma and other Republicans is vague and probably insufficient. Meanwhile, criticism of the act, signed into law last week by Gov. Mike Pence (R), continued to mount.

All eyes are on Indiana after Governor Mike Pence (R) signed a controversial religious freedom bill into law. The Post’s Sarah Pulliam Bailey explains what exactly is in the law and why both sides are so vocal. (Pamela Kirkland/The Washington Post)

Apple chief executive Tim Cook condemned the law in an op-ed in The Washington Post. Virginia Gov. Terry McAuliffe (D) wrote a letter to the Indianapolis Star inviting business leaders troubled by the law to move to Virginia. The president of the NCAA hinted that the Indiana-based athletic organization may stop holding major events there. And the rock band Wilco canceled a May 7 show in Indianapolis.

In addition, the Star devoted its entire front page Tuesday to an editorial about the law under the headline “FIX THIS NOW.”

The pressure was reverberating in other states, where some GOP leaders postponed consideration of their own religious freedom laws or disavowed them outright.

In Georgia, lawmakers canceled a hearing set for Monday morning on their version of the bill. In Arkansas, lawmakers debated tweaking a bill that passed the Senate last week, perhaps limiting its reach. And in North Carolina, Gov. Pat McCrory (R) said he was not inclined to sign a bill working its way through the statehouse. “What is the problem they’re trying to solve?” he asked Monday on WFAE’s “Charlotte Talks” radio program. The bill, he said, would “make no sense.”

The debate injected a divisive new issue into the 2016 presidential campaign, presenting Republican hopefuls with a difficult choice: publicly back Pence on an issue that threatens to hurt the GOP among the majority of Americans who support gay rights, or side with the party’s business wing against the law and risk angering base conservatives.

In recent days, former Florida governor Jeb Bush, Sen. Marco Rubio (Fla.), former Texas governor Rick Perry and Louisiana Gov. Bobby Jindal have all spoken approvingly of the law; Wisconsin Gov. Scott Walker has been more circumspect. Likely Democratic presidential candidate Hillary Rodham Clinton has criticized it.

The debate also shines a spotlight on other Religious Freedom Restoration Acts, which are in force at the federal level and in 19 states other than Indiana. The federal law was signed in 1993 by President Bill Clinton, a Democrat, and state versions have had broad support from both parties.

The current batch of religious liberties bills has been more controversial, in part because of the timing. Same-sex marriage is rapidly becoming the norm, with such unions legal in 37 states and the District. Last year, Arizona passed a similar law after a New Mexico photography company was sanctioned for refusing to take pictures for a lesbian commitment ceremony. But that bill sparked nationwide protests, drew criticism from the National Football League and was ultimately vetoed.

But the new laws are also fundamentally different. The federal law protects only individuals seeking relief from government intrusions on their religious beliefs. The Indiana law and others like it also apply to disputes between private parties.

University of Virginia law professor Douglas Laycock, one of the nation’s leading law-and-religion scholars, said “religious freedom” has become a catchphrase since last year’s Supreme Court ruling in the Hobby Lobby case. The court found that business owners who object to certain contraceptives on religious grounds may decline to provide them through their employee health plans.

“There’s bad behavior on both sides,” Laycock said. “Gay rights groups, as they become stronger and stronger and get more support for same-sex marriage, keep demanding more and more. Now they don’t want any religious exceptions for anybody.”

Meanwhile, he said, “Republican legislators are pandering to the base and saying we need to protect against gay marriage. These statements from the right fuel the outrage on the left.”

Bosma, the Indiana House speaker, said the law there has been misconstrued and is more limited than critics contend. For example, he said, it would not shield a dry cleaner who refused to serve a gay customer. “Both the opponents and proponents were indicating they felt that the language allowed a denial of services to gay Hoosiers,” Bosma said in an interview. “That definitely wasn’t the intent, nor do I believe was it the effect, but we intend to take action to make it clear.”

In an op-ed to be published Tuesday in the Wall Street Journal, Pence says the law “only provides a mechanism to address claims, not a license for private parties to deny services. Even a claim involving private individuals . . . must show that one’s religious beliefs were ‘substantially burdened’ and not in service to a broader government interest — which preventing discrimination certainly is.

Opponents note, however, that the law comes just months after a judge ordered same-sex marriage to be made legal in the state. And they note that Indiana does not include sexual orientation or gender identity as categories that are protected from discrimination under civil rights statutes — something they’d like to see addressed as part of the legislature’s fix.

The issue could have tremendous economic consequences in Indiana. Many companies have expressed displeasure with the law, including drugmaker Eli Lilly, one of the state’s largest employers and a frequent donor to local political candidates. Angie’s List, also based in Indiana, has halted expansion plans over the act. Monday, Gap and Levi Strauss & Co. announced their opposition to Indiana’s law and similar proposals.

Gay rights activists are hoping for similar reactions in other states. The Human Rights Campaign, a prominent gay rights group, has asked the NFL to deny Atlanta’s bid to host the 2019 Super Bowl. It also launched an advertising campaign warning Hollywood studios filming in Georgia that the state is “writing off LGBT people.” And a full-page ad in the San Jose Mercury News takes aim at Silicon Valley companies considering investments in Arkansas.

“Arkansas wants your business,” the ad says, “but at what price?”

Arkansas Gov. Asa Hutchinson (R) said he intends to sign that state’s religious freedom bill, which could come to a House vote this week. In a statement Monday, Hutchinson said he was “pleased that the legislature is continuing to look at ways to assure balance and fairness in the legislation.”

However, he said, “if this bill reaches my desk in similar form as to what has been passed in 20 other states, then I will sign it.”

Adam Talbot, a spokesman for the Human Rights Campaign, cautioned Hutchinson to rethink that stance.

“The governor should take note of what’s happening across the country,” Talbot said. “People don’t want this. People don’t need this. People think it’s dangerous. And there’s still time to stop it.”

Sarah Pulliam Bailey contributed to this report.