Some of those groups objected to providing coverage for any of the approved forms of contraception. Others objected to contraception they said was tantamount to abortion, though there are substantial questions about whether that characterization was correct as a matter of science.

The Trump administration took the side of the religious employers, saying that requiring contraception coverage can impose a “substantial burden” on the exercise of religion. The regulations it has promulgated made good on a campaign pledge by President Trump, who has said that employers should not be “bullied by the federal government because of their religious beliefs.”

The new regulations also included an exception for employers “with sincerely held moral convictions opposed to coverage of some or all contraceptive or sterilization methods.”

The states of Pennsylvania and New Jersey challenged the rules, saying they would have to shoulder much of the cost of providing contraceptives to women who lost coverage under the Trump administration’s rules.

In May, a unanimous three-judge panel of the United States Court of Appeals for the Third Circuit, in Philadelphia, blocked the regulations, issuing a nationwide preliminary injunction. Making exceptions to the requirement that employers provide women with coverage of contraception at no cost would have a large practical effect, Judge Patty Shwartz wrote for the panel. Citing government data, she wrote that about 70,000 to 126,000 women would lose contraceptive coverage if their employers could invoke the religious exemption.

That, in turn, she wrote, would disproportionately affect access to contraception for poor women.

“Cost is a significant barrier to contraceptive use and access,” she wrote. “The most effective forms of contraceptives are the most expensive. After the A.C.A. removed cost barriers, women switched to the more effective and expensive methods of contraception.”

The coverage requirement, sometimes called the contraceptive mandate, has been the subject of much litigation, reaching the Supreme Court twice.