Governor Asa Hutchinson, who previously said he would sign the Religious Freedom Restoration Act, noted that his own son had asked him to veto it, adding a personal element to the pressure to reject the bill.
On Wednesday, the state Senate sent to the House of Representatives legislation that would bring the act into line with federal statutes. A House panel is due to take up that law on Thursday.
Earlier this week, Indiana Governor Mike Pence said lawmakers should fix a similar Religious Freedom Restoration Act. After it was enacted last week, Indiana was hit with protests and boycotts, as well as warnings from powerful American businesses.