The Religious Freedom Restoration Act prohibits state or local governments from preventing individuals from practicing their religion, within certain boundaries.
The state’s Republican Governor signed the legislation last week.
As many as 3000 people joined a rally on Saturday in protest. Critics have argued the law could give businesses a legal loophole for refusing to serve gay men and women on the grounds of religious beliefs.
Apple CEO Tim Cook, is among the law’s high-profile critics.
"We are deeply disappointed in Indiana's new law and calling on Arkansas Gov. to veto [similar laws]," he wrote on Twitter.
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The openly gay mayor of Seattle has banned city employees from travelling to the state on official business, saying he didn’t want taxpayer dollars to fund discriminatory laws.
