Washington ? The Supreme Court dealt a setback to President Obama’s health-care law Monday and ruled that Christian business owners with religious objections to certain forms of birth control may refuse to provide their employees with insurance coverage for contraceptives.

In a major 5-4 ruling on religious freedom, the justices decided the religious rights of these company owners trump the rights of female employees to receive the full contraceptive coverage promised by the law.

The decision, written by Justice Samuel A. Alito Jr., is a victory for social conservatives. It also could open the door for other businesses to claim a religious exemption from laws, including anti-discrimination measures that protects gays and lesbians.

The administration’s lawyers had argued that a private, for-profit corporation, like the Hobby Lobby chain of arts and crafts stores, had never before been accorded rights based on religion.

But the court determined that the Green family from Oklahoma City that founded the chain has a sincere religious belief that certain contraceptives destroy a fertilized egg and, therefore, are akin to an early abortion.

Two years ago, the court narrowly upheld the Affordable Care Act as constitutional on a 5-4 vote. Today’s decision will limit one aspect of the health-care law — the requirement that health plans include coverage for contraceptives. But it’s one that could potentially affect large numbers of women employees.

It is unclear how many business owners will seek to opt out of providing contraceptives based on their religious views.

The contraceptive requirement was challenged by a pair of family-run businesses whose owners said they believe that so-called “morning-after” pills and intrauterine devices can effectively abort a fertilized egg. They said the rule requiring them to pay for the coverage made them complicit in sin.

The Obama administration told the justices that contraceptives are necessary preventive care for women and that their availability would help reduce unwanted pregnancies and abortions.

The cases are Burwell v. Hobby Lobby Stores Inc. and Conestoga Wood Specialties Corp. v. Burwell.