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In a letter signed by dozens of religious representatives, including from the Catholic, Protestant and Mormon churches, the leaders said the matter goes beyond contraceptives and touches on fundamental conscience rights.

Dozens of businesses have sued to try to halt the Obama contraceptive policy. On Friday, the 10th U.S. Circuit Court of Appeals issued a temporary restraining order exempting Hobby Lobby Stores, a crafts company based in Oklahoma, from the mandate while its case winds its way through the courts.

But the lawsuits could take some time to reach final decisions. Mr. Moore said that means the battle over the mandate may shift to Congress.

The Obama administration has drawn up a three-tier policy that would exempt churches and other actual houses of worship from the requirement altogether; grant faith-based nonprofits an accommodation to divorce themselves from the mandate by not having to manage or pay for the contraceptives; and give for-profit entities no relief. All other businesses would have to provide regular coverage.

Challengers particularly object to having to cover contraceptives taken after sex, such as Plan B or Ella, which they say can sometimes act as an abortifacient by preventing implantation of a fertilized egg.