A federal appeals court has refused to grant Catholic groups in Michigan and Tennessee an injunction that could have exempted them from the Affordable Care Act's contraception mandate.

In its opinion Wednesday, the 6th U.S. Circuit Court of Appeals wrote that all plaintiffs are already eligible for an exemption or an accommodation.

An accommodation to the mandate still allows employees to receive contraceptive coverage, but it's paid for and administered by an insurance issuer or third-party administrator.

The Catholic groups say, regardless, the mandate could make them "complicit in a great moral wrong."