WASHINGTON — The Supreme Court on Monday said it will consider next term whether a Denver baker unlawfully discriminated against a gay couple by refusing to sell them a wedding cake.

Lower courts had ruled that Jack Phillips, the owner of Masterpiece Cakeshop, had violated Colorado’s public accommodations law, which prohibits refusing service to customers based on factors such as race, sex, marital status or sexual orientation.

There are similar lawsuits from florists, calligraphers and others who say their religious beliefs won’t allow them to provide services for same-sex weddings. But they have found little success in the courts, which have ruled that public businesses must comply with state anti-discrimination laws.

The court granted the case after weeks of considering it. In 2014, the justices declined to revisit a New Mexico Supreme Court decision that found that a photographer violated a state civil rights law when she declined to photograph a lesbian couple’s commitment ceremony.

Since then, the high court has found that marriage is a fundamental right that states may not prohibit to gay couples.

The Washington Supreme Court found that Barronelle Stutzman, owner of Arlene’s Flowers in Richland, Wash., violated a state civil rights law that bars discrimination in public businesses on the basis of sexual orientation. The court also ruled that the law does not infringe on her free speech.

The Texas Supreme Court is considering a challenge to Houston’s provision that gives the same benefits to spouses of gay workers as it does to those of straight workers. Gay rights activists say the Supreme Court’s 2015 landmark decision in Obergefell v. Hodges should have settled the issue.

In the Colorado case, David Mullins and Charlie Craig visited Masterpiece Cakeshop in July 2012, along with Craig’s mother, to order a cake for their upcoming wedding reception. Mullins and Craig planned to marry in Massachusetts, where same-sex marriages were legal at the time, and then hold a reception in Colorado.

But Phillips refused to discuss the issue, saying his religious beliefs would not allow him to have anything to do with same-sex marriage. He said other bakeries would accommodate them.

The couple filed a complaint, and in 2014, the Colorado Civil Rights Commission determined that Phillips’s action violated state law. That ruling was upheld in Colorado state courts.