INDIANAPOLIS — Two states roiled by criticism over new religious objections laws are looking to move forward after taking different approaches to changing the legislation to ease concerns about discrimination.

The governors of Indiana and Arkansas signed bills Thursday that lawmakers hoped would quiet the national uproar over whether the laws offered a legal defense for discrimination against gays.

For Arkansas, the changes requested by Gov. Asa Hutchinson amid mounting criticism from retail giant Wal-Mart and other businesses meant revising the language to closely align with that in the 1993 federal Religious Freedom Restoration Act. But for Indiana, which had seen businesses and organizations ban travel and cancel conventions, the solution was an amendment that put the first references to sexual orientation and gender identity into state law.

Indiana Gov. Mike Pence, who said the law was never intended to allow discrimination and blamed the fallout on “mischaracterizations” of the legislation, signed the bill privately Thursday and urged residents to move on.