In another significant denial, the court also Monday rejected a challenge to a longstanding ban on campaign contributions by corporations. Both rulings came without comment.
The justices left in place a New Mexico Supreme Court ruling that said Elane Photography violated a state anti-discrimination law when it refused a request by a lesbian couple in 2007 to be their official photographer for their commitment ceremony.
The studio's owners, Elaine and Jonathan Huguenin, owners of Elane Photography, said they had agreed to take portrait photos of the couple. But they said taking photos of the ceremony would conflict with her religious beliefs and violated the First Amendment's ban on compelled speech.
The high court's move comes after Mississippi Gov. Phil Bryant last week signed a controversial bill into law that allows residents to sue over laws they say place a substantial burden on their religious practices. Critics say the measure is a thinly veiled attempt to allow people and businesses to discriminate against gays.
In Arizona, a similar bill passed the state's Republican-controlled legislature in February but was vetoed by Republican Gov. Jan Brewer.
The Supreme Court also left in place a lower court ruling that upheld the federal ban on direct contributions by corporations to candidates in federal elections. The Iowa Right to Life group argued that corporations have the same constitutional free speech rights as individuals to make campaign donations.
The denial in the Iowa case appeared to suggest the justices either found the new case didn't present the issue adequately or weren't ready to consider extending its ruling in McCutcheon to other donation restrictions, Lyle Denniston wrote on the website SCOTUSblog.