Indiana Gov. Mike Pence (R) told the Indianapolis Star's Tim Swarens that he's in discussions with legislators to potentially clarify a controversial religious freedom law so that it won't promote discrimination against LGBT people. The law, which Pence signed on Thursday, has come under fire for potentially protecting employers, landlords, and business owners who discriminate against LGBT people on religious grounds. "[T]his law is not about discrimination," Pence told Swarens. "It's about protecting religious liberty and giving people full access to the judicial system." Businesses and public figures around the country, including Angie's List and George Takei, have criticized the religious freedom law as discriminatory. Pence's comments appear to come in response to that public pressure. It's unclear how, exactly, legislators will alter the religious freedom law. Pence later told ABC News's George Stephanopoulos, "We're not going to change the law, okay? But if the general assembly in Indiana sends me a bill that adds a section that reiterates and amplifies and clarifies what the law really is, and what it has been for the last 20 years, than I'm open to that."

Indiana is one of dozens of states pushing laws that could limit LGBT rights

Indiana's law is among the latest in a series of measures Republicans are proposing at the state level that could limit LGBT rights.

Supporters insist the purpose of the religious freedom laws is to protect religious rights, not allow discrimination against LGBT residents. The measures create additional legal protections that allow residents to challenge laws or regulations that they believe violate their religious freedoms.

But critics of the laws worry the measures will allow anti-LGBT discrimination even if that's not their intent. They point to a 2014 Supreme Court decision that cited the federal religious freedom law to exempt some employers with religious objections from Obamacare's birth control mandate. A similar ruling could be applied to any local, state, and federal laws that protect LGBT people from discrimination in the workplace, housing, and public accommodations (hotels, restaurants, and other places that serve the general public).

Asked if the clarification to Indiana's law will add explicit legal protections for gay and lesbian Indianans, Pence reportedly said, "That's not on my agenda." The comment led some LGBT activists, including Ian Thompson at the ACLU, to question Pence's motives.

If #SB101 wasn't intended to provide a license to discriminate why not make explicit that it can't be used for that purpose, @GovPenceIN? — Ian Thompson (@iantDC) March 29, 2015

This so-called clarification to #SB101 sounds like an effort by @GovPenceIN to save face that won't mean a hill of beans to #LGBT Hoosiers. — Ian Thompson (@iantDC) March 29, 2015

Two types of laws that could limit LGBT rights have passed since the beginning of 2015: the religious freedom law in Indiana, and a law in Arkansas that effectively nullifies municipalities' nondiscrimination protections for LGBT people. Both laws, advocates say, could open LGBT people to discrimination in the workplace, housing, and public accommodations.

Most states don't protect LGBT people from discrimination in these settings, meaning people can potentially be legally fired from their jobs, evicted from their homes, or kicked out of a business just because of their sexual orientation or gender identity. Some advocates argue the Civil Rights Act of 1964 already shields LGBT workers from workplace discrimination, but the argument has yet to be proven in court.

Watch: How most states still discriminate against LGBT people

Further reading: Indiana's religious freedom law shows the new frontier in the battle over LGBT rights.