WASHINGTON (Reuters) - Businesses better have good evidence to back up claims of health benefits from their products, the U.S. Federal Trade Commission said on Monday after the Supreme Court rejected POM Wonderful's challenge to FTC findings that the juice maker's advertising was misleading.

The Supreme Court left in place a lower-court ruling that largely upheld the regulatory agency's determination about the pomegranate juice maker's advertising claims that its products fight ailments such as heart disease, prostate cancer and erectile dysfunction.

"The outcome of this case makes clear that companies like POM making serious health claims about food and nutritional supplement products must have rigorous scientific evidence to back them up," FTC Chairwoman Edith Ramirez said in a statement.

The FTC said POM could state that its juice treated or prevented disease only if the claim was backed by at least one randomized, controlled clinical trial using human subjects. Other claims of health benefits must be backed by "competent and reliable scientific evidence," the FTC added.

POM spokesman Steven Clark said that "we continue to stand behind our efforts to publicly convey valuable information about the health benefits of POM."

The U.S. Court of Appeals for the District of Columbia Circuit ruled last year that POM Wonderful could not advertise that its pomegranate drinks treat or prevent heart disease or other medical conditions unless it has proof, upholding the FTC's 2010 order.

The advertisements that the FTC challenged appeared in Parade, Fitness and Prevention magazines, as well as online and on product tags, the FTC said.

"Many of those ads mischaracterized the scientific evidence concerning the health benefits of POM's products with regard to those diseases. The FTC Act proscribes - and the First Amendment does not protect - deceptive and misleading advertisements," the appeals court said in its ruling, referring to the U.S. Constitution's protection of free speech.

The advertisements that most concerned the FTC were discontinued in 2005 and others were halted in 2007, POM's lawyers said.

The case is POM Wonderful v. FTC, U.S. Supreme Court, No. 15-525.

(Reporting by Lawrence Hurley; Additional reporting by Diane Bartz; Editing by Will Dunham)