INDIANAPOLIS — Indiana Gov. Mike Pence asked lawmakers Tuesday to send him a clarification of the state’s new religious-freedom law later this week, while Arkansas legislators passed a similar measure, despite criticism that it is a thinly disguised attempt to permit discrimination against gays.

The Arkansas proposal now goes to Republican Gov. Asa Hutchinson, who has said he will sign it.

Pence defended the Indiana law as a vehicle to protect religious liberty but said he has been meeting with lawmakers “around the clock” to address concerns that it would allow businesses to deny services to gay customers.

The governor said he does not believe “for a minute” that lawmakers intended “to create a license to discriminate.”

“It certainly wasn’t my intent,” said Pence, who signed the law last week.

But, he said, he “can appreciate that that’s become the perception, not just here in Indiana but all across the country. We need to confront that.”

The Indiana law prohibits any laws that “substantially burden” a person’s ability to follow his or her religious beliefs. The definition of “person” includes religious institutions, businesses and associations.

Although the legal language does not specifically mention gays and lesbians, critics say the law is designed to shield businesses and individuals who do not want to serve gays and lesbians, such as florists or caterers who might be hired for a same-sex wedding.

In Washington, White House spokesman Josh Earnest said Indiana officials appeared to be in “damage-control mode” following the uproar over the law.

Earnest also took issue with Pence’s claim that Indiana’s law was rooted in a 1993 federal law. He said the Indiana measure marked a “significant expansion” over that law because it applies to private transactions beyond those involving the federal government.

The federal Religious Freedom Restoration Act arose from a case related to the use of peyote in a Native American ritual. But in 1997, the U.S. Supreme Court ruled that the federal law did not apply to the states. So states began enacting their own laws. Twenty now have them on the books.

Businesses and organizations including Apple and the NCAA have voiced concern over Indiana’s law, and some states have barred government-funded travel to the state.

Democratic legislative leaders said a clarification would not be enough.

“To say anything less than a repeal is going to fix it is incorrect,” House Minority Leader Scott Pelath said.

Republican Senate President Pro Tem David Long said lawmakers were negotiating a clarification proposal that he hoped would be ready for public release on Wednesday, followed by a vote Thursday before sending the package to the governor.