Justice Samuel A. Alito Jr. on Tuesday renewed his criticisms of the Supreme Court’s landmark decision recognizing the right to same-sex marriage, saying that people who oppose homosexuality risk being unfairly “labeled as bigots and treated as such.”

The justice included his warning in a five-page statement explaining why the court had rejected a request to hear a Missouri case about people removed from a jury after voicing religious objections to gay relationships. The case, Justice Alito wrote, “exemplifies the danger” from the court’s 2015 decision, Obergefell v. Hodges.

The ruling, he added, shows how “Americans who do not hide their adherence to traditional religious beliefs about homosexual conduct will be ‘labeled as bigots and treated as such’ by the government.”

The statement appeared to offer a glimpse into Justice Alito’s continued discontent with Obergefell v. Hodges, in which the court, by a 5-to-4 vote, guaranteed a right to same-sex marriage, a long-sought victory in the gay rights movement.

In the years since, Justice Alito and Justice Clarence Thomas, who both dissented from the 2015 decision, have appeared to urge the court to reconsider the ruling. The court, they have contended, invented a right not based in the text of the Constitution; they said it had cast “people of good will as bigots.”

Only two members of the court who ruled in favor of Obergefell remain on the bench — Justices Sonia Sotomayor and Elena Kagan. The court has since transformed under the presidency of Donald J. Trump with the addition of three conservative justices who have solidified a conservative supermajority.