After initially telegraphing optimism about President Obama’s decision Friday to amend the religious exemption for mandatory birth-control and sterilization coverage, the U.S. Conference of Catholic Bishops has declared total opposition to any compromise on the issue.

The organization wrote that it will continue pushing for a complete end to the birth-control mandate “with no less vigor, no less sense of urgency” than before the Obama administration decided to let nonprofit church-affiliated employers such as hospitals and universities, and not just churches, technically opt out of the requirement.

“The only complete solution to this religious liberty problem is for [the U.S. Department of Health and Human Services] to rescind the mandate of these objectionable services,” the conference said in a statement released late Friday.

Just hours before, Cardinal-designate Timothy Michael Dolan of New York, who heads the conference, said he saw “initial opportunities in preserving the principle of religious freedom” in Obama’s action. He also called it “a first step in the right direction.”

The bishops’ broadside is evidence that Obama’s effort to limit the damage from this unusually complicated moral, legal, medical and financial issue isn’t necessarily working. Most of the Republican presidential candidates have hammered Obama for what they contend is a trampling of religious freedom. Even many of the president’s supporters believe that the original exemption was too narrow and the policymaking handled clumsily — although they supported the amendment announced Friday.

An administration official not authorized to speak on the record expressed little surprise at the bishops’ statement, which if anything represents a hardening of their position.

“We never anticipated that this announcement would win the endorsement of an organization that opposed health reform from the very beginning,” the official said. “But we believe it’s the right way to fully address concerns about religious liberty and ensure women get the coverage they need.”

The dispute concerns the requirement under the Obama-sponsored 2010 health-care law that certain “preventive services” be included in all health insurance plans, with no out-of-pocket charges to the person insured.

The administration announced in August that contraception and sterilization would be among those services. It also said that churches with a moral objection to pharmacological birth control would not be required to offer that coverage to employees.

Many organizations and experts — Catholic and otherwise — contended that the exemption was not broad enough.

Last month the administration said nonprofit religious-affiliated organizations not offering contraception and sterilization coverage in their health plans would have an extra year — until August 2013 — to comply with the mandate. However, critics said the delay did nothing to address the moral objections.

On Friday, Obama announced that nonprofit church-affiliated entities would be able to opt out in a particular way. They would not have to provide contraception in their health plans, but female employees wanting coverage could obtain it directly from the insurance companies. The arrangement would not add any cost to the employee’s premium, the argument being that prevention of childbirth is cheaper than childbirth.

In their statement, however, the bishops say that among the groups needing “clear protection” from the contraception mandate are “religious and secular for-profit employers.” That would sweep in a far larger variety of organizations.

Richard M. Doerflinger, an official of the U.S. Conference of Catholic Biships, was asked whether that meant that a Catholic owner of a sporting-goods store who believed that use of birth-control pills is immoral should be able to offer health insurance excluding that coverage. He said it did.

“That person should have the freedom to choose the health plan that does not violate his convictions. It doesn’t mean he will be able to find it, but the government shouldn’t have anything to say about it,” Doerflinger said Saturday.

In addition, religiously affiliated insurance companies are not exempt from the mandate. Friday’s announcement also left unresolved what a Catholic-affiliated organization that self-insures and objects to contraception would do, as there is no insurance company to provide coverage directly to employees.

Objections to the compromise came from quarters other than the bishops.

It drew a swift rebuke from Jim Towey, who headed President George W. Bush’s faith-based office and is now president of Ave Maria University, a conservative Catholic school near Naples, Fla.

“We subsidize these health plans, so the question is whether university resources are underwriting this,” Towey said.

“I still don’t think President Obama gets it,” Towey added. “This is a fig leaf of a political compromise that’s trying to have it both ways, to mollify women’s groups and so-called centrist Catholics. But I think, fundamentally, this is not the end of this debate. It’s just the beginning.”

He said the university board planned to meet Monday to discuss legal action against the new mandate.

Some Catholic organizations, however, appeared satisfied by Obama’s action. The head of the Catholic Health Association of the United States, Sister Carol Keehan, said the “framework developed has responded to the issues we identified that needed to be fixed.

The administration official said that “we will start, in the coming days, by convening a series of meetings with faith community leaders to explore solutions.” He said the bishops will be invited.

Staff writers Peter Wallsten and N.C. Aizenman contributed to this report.