Lawmakers in Indiana and Arkansas plan on Thursday to remedy religion acts that were sent back to them this week following criticism from rights activists and businesses who said the measures allowed discrimination against gays.
The Arkansas Senate took up the challenge late on Wednesday, sending legislation to the House of Representatives that would bring its Religious Freedom Restoration Act (RFRA) into line with federal statutes.
A House panel is due to take up that law on Thursday.
Indiana's governor said lawmakers should fix a similar RFRA. After it was enacted last week, the state was hit with protests, threatened boycotts and warnings from powerful U.S. firms of pending economic damage for standing against U.S. ideals of inclusion.
Twenty U.S. states and the federal government have RFRAs, which allow individuals to sue the government if they believe their First Amendment religious rights have been violated.
But those in Indiana and Arkansas go further than all but one of the state laws, allowing lawsuits between private parties.
That raised the possibility of businesses such as realtors using the law as a defense if they are sued for refusing to show homes to a member of the lesbian, gay, bisexual and transgender (LGBT) community.