Indiana Republican leaders on Monday vowed to “clarify” a new religious liberties law after an onslaught of criticism from celebrities and businesses who say it and other laws being considered around the nation essentially legalize discrimination against gay, bisexual and transgender people.

But gay rights groups said a promise of a vague “fix” was not enough, demanding more explicit actions that protect gays from bias.

The proposal is the latest development in the flare-up over Indiana’s Religious Freedom Restoration Act, which Gov. Mike Pence (R) signed into law last week, unleashing a torrent of criticism. On Monday, Apple chief executive Tim Cook joined the chorus, writing a Washington Post opinion piece calling it and similar laws “dangerous.” The essay followed an announcement by Indiana-based Angie’s List that it was holding off on expansion plans there as a result, as well as outraged expressions from the NCAA, NBA and WNBA, among others.

The furor had intensified on Sunday after Pence refused on ABC’s “This Week” to say whether the law permitted businesses to refuse services to gay people. The appearance prompted Republicans to seek a solution, Indiana House Speaker Brian Bosma (R) said Monday in an interview.

“After a lot of discussions this weekend, and the governor’s failure to say ‘no’ when asked if the intent of the legislation was to discriminate, we thought it important to [clarify that] no discriminatory intent was meant, nor can we let that occur,” he said. “We intend to amend that language to make it crystal clear that no discrimination occurs.”

Bosma said the legislature was working on language, which could be ready this week.

But gay rights groups said the promise, while a positive step, was not enough. They asked for an update to the state’s civil rights statutes to include gay and transgender people as protected classes and demanded explicit language in the new law asserting that it cannot be used to undermine local or statewide civil rights protections.

“Since last week, Indiana’s economy and our reputation has suffered — in a big way. And for every second RFRA remains on the books in its current discriminatory form, the backlash will only worsen,” Freedom Indiana, a coalition of gay rights groups, wrote on its Web site.