Most church-affiliated organizations will be required to offer their workers coverage of birth control as part of their health plans, the Obama administration announced Friday, but they can get more time than other employers to comply.

The decision came as a bitter disappointment to organizations ranging from the U.S. Conference of Catholic Bishops to the National Association of Evangelicals, which had lobbied hard for a broad exemption for employers that oppose birth control on religious grounds.

“This is nothing less than a direct attack on religion and First Amendment rights,” said Franciscan Sister Jane Marie Klein, head of a system of 13 Catholic hospitals in Indiana and Illinois.

The rule, which was first announced last summer and which has drawn more than 200,000 comments, requires private insurance not merely to include birth control, but to do so without out-of-pocket charges. It will take effect beginning Aug. 1, as plans renew.

From the beginning, the rule exempted employers such as churches whose primary purpose is to inculcate religious beliefs and that mainly employ and serve individuals who share those beliefs. Religious advocates argued that this definition was too narrow, excluding a wide range of church-affiliated universities, hospitals and schools.

On Friday, Health and Human Services Secretary Kathleen Sebelius unveiled a small change: Religious organizations will be allowed an extra year to comply with the requirement. But the rule itself and the types of employers covered by it will remain unchanged, she said.

The delay was no consolation to Cardinal-designate Timothy M. Dolan, archbishop of New York and president of the U.S. Conference of Catholic Bishops. “In effect, the president is saying we have a year to figure out how to violate our consciences,” he said. “The Obama administration has now drawn an unprecedented line in the sand.”

Sebelius portrayed the delay option as a reasonable compromise between competing interests. “This . . . strikes a balance between respecting religious freedom and increasing access to important preventive services,” she said in a statement.

Many women’s groups and Democratic lawmakers greeted the decision with relief. They had feared the administration was planning to significantly broaden the religious exemption.

“This is good news for millions of women whose access to contraceptive services under this new benefit was being questioned,” said Sen. Patty Murray (D-Wash.).

Dolan had raised the exemption issue directly with President Obama in November. Following that meeting, word began to spread that the administration was considering ways to address the bishops’ concerns.

Democratic lawmakers who are advocates of women’s reproductive rights launched a vigorous counteroffensive — venting their outrage in several conference calls with top White House advisers and, in the case of at least one senator, Sen. Jeanne Shaheen (D-N.H.), lobbying the president in person.

On Friday, those lawmakers pronounced themselves thrilled.

“This decision marks a tremendous victory,” said Rep. Lois Capps (D-Calif.). “For years there has been a relentless campaign to politicize women’s health issues and it is endangering the health of women and their families. The administration deserves credit for standing its ground and following the science.”

Birth control is the most commonly prescribed drug for women age 18 to 44, and polls suggest that large majorities of Americans of all faiths support its use.

The rule requiring its inclusion in health plans fleshes out a more general provision in the 2010 health-care law mandating that all new insurance policies cover preventive services without co-pays or other out-of-pocket charges. These must include a range of services particular to women.

Sebelius has specified that the list will contain all forms of birth control approved by the Food and Drug Administration, including methods that are controversial — such as the emergency contraceptives Plan B and Ella, commonly referred to as “morning-after pills,” as well as sterilization.

The one-year delay option announced Friday will not be available to religious institutions that already offer some degree of contraception coverage — including many Catholic universities and hospitals in states that have their own birth control requirements. Church-affiliated universities also cannot postpone offering contraception coverage to their students, as opposed to their workers, regardless of whether they currently provide it.

To qualify for the delay, an institution must certify to federal authorities that it is a nonprofit organization and that, for religious reasons, it does not presently offer contraception to its workers. The employer must also notify employees that birth control is available through other sources such as community health centers, public clinics and hospitals, with support provided to low-income patients who might otherwise have difficulty paying for it.

Once the extra year has expired, the employer could presumably avoid covering birth control by ceasing to offer workers health insurance altogether. But if any of the workers need government assistance to purchase insurance on their own, the employer would then face steep fines.

It is unclear how many women will be affected by the delay because there are not reliable estimates of the numbers employed by church-affiliated instiutions. It is also not known how many of these individuals and their dependents get health insurance through such employers.

Administration officials said Friday that the delay was offered in response to complaints by religious organizations that it would be difficult to comply with the rule within a matter of months.

But several religious leaders interviewed Friday ridiculed that explanation.

“This is not a logistical matter. This is a matter of conscience,” said Dennis Brown, spokesman for the University of Notre Dame, a Catholic institution.

Galen Carey, head of government relations for the National Association of Evangelicals, agreed but said the delay would at least prove “minimally helpful” in one regard: “It gives those groups that are affected more time to pursue litigation to overturn this. And, of course, it pushes the ultimate decision into the next administration, which, if it’s a new administration, possibly would reverse this.”

Already, a college and a university have filed lawsuits in federal courts challenging the constitutionality of the birth control rule. They are represented by the Becket Fund for Religious Liberty, a nonprofit firm that was also counsel to the winning side of the Supreme Court’s recent finding that churches are exempt from employment discrimination suits by their ministers.