More than 300 demonstrators protested Sunday against a Mississippi law that targets the LGBT community.

The protesters marched from the state Capitol to the governor's mansion in Jackson.

Mississippi's law, House Bill 1523, allows businesses to deny services to LGBT people based on their “sincerely held religious beliefs or moral convictions.”

Human Rights Campaign (HRC) President Chad Griffin led the crowd in chanting “Shame on you” outside Governor Phil Bryant's residence.

“We need to show him loud and clear we're not going away,” he told the crowd.

Bryant has defended the law, saying that it is needed to balance the scales of justice.

“[W]e believe the scales of justice must be balanced for those people of faith and those that have other ideas about their desires in life. And that's what the scales of justice must do, is be balanced. And we believe that this is a step in protecting the civil liberties of people of faith just as the First Amendment of the Constitution does,” he said during a recent radio appearance.

Last week, opponents of the law, which takes effect July 1, said that it might violate the federal order that struck down Mississippi's ban on same-sex marriage.

(Related: Lawyer who challenged Mississippi's gay marriage ban says new law may violate order.)