Clarification: Earlier versions of this article said "federal courts" that have considered challenges from business owners opposed to the Affordable Care Act’s contraceptives mandate have split their decisions, two granting injunctions and two denying. Those numbers refer to the four circuit courts of appeal that have ruled on injunction requests from the private employers. The article has been updated.

The Obama administration proposed new rules Friday that would guarantee widespread access to contraceptives under the Affordable Care Act, but seemed unlikely to head off legal battles that could return a part of the health-care law to the Supreme Court.

The regulations allow religious nonprofit organizations that morally object to contraceptives to not offer that benefit for their employees. But their workers would receive a stand-alone private insurance policy providing birth control coverage at no cost.

Some religious groups criticized the proposed rules. For more than a year, they have mounted a high-profile protest and filed dozens of lawsuits against the contraceptive mandate, arguing that it is a violation of their religious freedom.

These nonprofits worry that their premium dollars might help pay for the stand-alone plans. Separately, some private businesses owned by individuals with strong religious objections to the mandate have sued because they don’t want to provide contraceptive coverage to their workers.

“We were extremely disappointed with this inadequate proposal,” said Kyle Duncan, general counsel for the Becket Fund for Religious Liberty. His group represents both private employers and faith-based nonprofits. “This is not what many of our clients were hoping and praying for: That they would be given a way of not being subject to the mandate at all.”

The required coverage of contraceptives has proved a vexing challenge for the Obama administration. Its attempt to strike a satisfying balance between reproductive health coverage and religious freedom became a key campaign issue.

Women’s health groups, which have been vociferous advocates of the contraceptives provision, quickly lauded the administration’s decision.

“Today’s draft regulation affirms yet again the Obama administration’s commitment to fulfilling the full promise of its historic contraception policy,” NARAL Pro-Choice America President Ilyse Hogue said. “Thanks to this commitment, most American women will get birth-control coverage without extra expense. Increased access to birth control is a huge win for women.”

The Affordable Care Act initially required almost all employers to cover contraceptives as part of a larger package of preventive health benefits for women. Some religious groups opposed the requirement, which they argued would force them to go against their beliefs. Houses of worship, such as churches and synagogues, would be exempt.

Last February, the administration announced an accommodation for faith-based nonprofits: Insurance companies would cover the cost of contraceptive coverage.

Religious leaders derided the policy as an “accounting gimmick,” arguing that the premiums they pay to health insurers could end up paying for the contraceptives they oppose.

The compromise did not address large companies that self-insure, meaning they foot the bill for their employees’ health care rather than pay premiums to insurance plans. The Obama administration outlined a number of policy suggestions in March that could address those concerns. It included proposals such as contracting with a national insurance plan to provide coverage or tapping into other streams of federal dollars.

Under the policy proposed Friday, self-insured plans that decided to opt out of contraceptive coverage would notify the company that administers their health benefits. That third-party administrator would then be responsible for arranging “separate individual health insurance policies for contraceptive coverage from an issuer providing such policies,” according to the proposed regulation.

Insurers that create these plans for self-insured companies will receive an offset from the federal government: lower fees to sell plans on the new health exchanges run by the administration.

Reaction from Catholic institutions seemed cautious. Cardinal Timothy Dolan, leader of the U.S. Conference of Catholic Bishops — essentially the spokesman for the U.S. church — said the bishops and their lawyers would review the new regulations.

“We welcome the opportunity to study the proposed regulations closely,” Dolan said in a statement issued midday Friday. “We look forward to issuing a more detailed statement later.”

Reactions reflected the diversity of views among Catholics.

The University of Notre Dame, a key battleground of American Catholicism, said in a statement that officials wouldn’t comment until they had studied the proposal more closely. Notre Dame stirred the ire of traditional Catholics when it honored President Obama in 2009 by giving him an honorary degree and hosting him as commencement speaker. Three years later, the school joined dozens of other mostly Catholic nonprofits in suing the administration over the mandate.

Liberal Catholic figures applauded the White House on Friday.

The Department of Health and Human Services and “the administration have gone out of their way to resolve the concerns of religious institutions that object to covering contraceptives in their insurance programs,” said the Rev. Thomas Reese, former editor of the prominent Catholic magazine America and a well-known writer. “They have also found creative ways to provide contraceptives to the employees of religious colleges and hospitals without the involvement of these institutions.”

In the District, the U.S. Court of Appeals has held off ruling on a lawsuit filed by two colleges — Belmont Abbey in Belmont, N.C., and Wheaton College in Wheaton, Ill. — as the Obama administration worked to issue the new rules. The same court dismissed a lawsuit brought by the Catholic Archdiocese of Washington on similar grounds.

Four U.S. circuit courts of appeal that have considered the separate challenges brought by business owners have split about whether they should have to comply with the law while it is being challenged. Two have granted business owners injunctions, while two others have denied similar appeals.