The Supreme Court on Wednesday struggled with the question of how to ensure access to birth control at no cost for women while respecting the religious beliefs of employers who say providing contraceptive coverage violates their faith.

The case is the latest dispute over the expansion of health-care benefits for women under the Affordable Care Act and pits religious liberty against a woman’s right to health care. Wednesday’s arguments markedthe third time the high court considered the contraceptive coverage requirement but the first since conservative justices Neil M. Gorsuch and Brett M. Kavanaugh joined the bench.

At issue is the Trump administration’s attempt in 2018 to expand the types of organizations that could opt out of providing cost-free access to birth control and the extent to which the government should create exemptions to the law for religious groups and nonreligious employers with moral and religious objections. The Obama administration had narrower exceptions for churches and other houses of worship, and created a system of “accommodations,” or workarounds, for religiously affiliated organizations such as hospitals and universities to avoid directly covering the cost of birth control.

Several justices, including Chief Justice John G. Roberts Jr. and Elena Kagan, questioned Wednesdaywhether the exemptions in the Trump administration’s new rules are too broad.

“I wonder why it doesn’t sweep too broadly,” Roberts asked the administration’s lawyer. “In other words, not everybody who seeks the protection from coverage has those same objections.”

The rule, Kagan added, “essentially scraps the existing accommodation even for employers who have no religious objection to it.”

Solicitor General Noel Francisco said in response that the accommodation is still available, just not mandatory. Employers who do not object, he said, are unlikely to seek an exemption because they would be depriving their employees of a “valuable benefit.”

Both Roberts and Justice Stephen G. Breyer expressed frustration that neither side had been able to reach a compromise since the issue was last before the high court in 2016.

“I don’t understand why this can’t be worked out,” Breyer said.

The high court held its arguments for the third consecutive day by conference call because of the coronavirus pandemic. With all nine justices taking turns asking questions of both sides for an hour and a half, it was difficult to predict the case’s eventual outcome.

If the new rules take effect, the government has said that between 70,500 and 126,400 women would lose access to cost-free birth control in one year.

Justices Ruth Bader Ginsburg and Sonia Sotomayor repeatedly expressed concerns about the possibility that tens of thousands of women could be left without no-cost access to birth control.

“The glaring feature of what the government has done in expanding this exemption is to toss to the winds entirely Congress’s instruction that women need and shall have seamless, no-cost, comprehensive coverage,” Ginsburg said. “This leaves the women to hunt for other government programs that might cover them.”

Francisco disagreed, telling the court that no part of the Affordable Care Actspecifically requires contraceptive coverage, but instead allows the administration to “decide whether or not to cover it in the first place.”

“And we think that that also includes the discretion to require that most employers provide it, but not the small number who have sincere conscientious objections,” he said.

Under the new rules, the employers able to opt out include essentially all nongovernmental workplaces, from small businesses to Fortune 500 companies. And the employer has the choice of whether to permit the workaround.

The states of Pennsylvania and New Jersey initially challenged the rules, noting that when women lose coverage from their employers, they seek state-funded programs and services. Last summer, a unanimous panel of the U.S. Court of Appeals for the 3rd Circuit blocked the rules from taking effect nationwide. The court said the administration probably lacked authority to issue such broad exemptions and did not comply with requirements to provide notice and allow public comment on the rules.

Justice Samuel A. Alito Jr. suggested Wednesday that the 3rd Circuit got it wrong. He pointed to the high court’s earlier decision that held if a person sincerely believes that it is immoral to perform an act that enables another person to commit an immoral act, “a federal court does not have the right to say that this person is wrong on the question of moral complicity.”

“That’s precisely the situation here,” Alito said.

Kavanaugh acknowledged the “very strong interests on both sides,” but suggested it was up to each administration to use its discretion in the absence of specific limits imposed by Congress.

As long as the agency has acted within reason, Kavanaugh said, “It seems to me the judicial role is not to put limits on the agency discretion that Congress has not put there.”

“Why isn’t this a reasonable way to balance it?” he asked the lawyer representing the state of Pennsylvania.

Chief Deputy Attorney General Michael Fischer said in response that the rules go well beyond what Congress envisioned. The rules, he said, provide “a grant of authority so broad it allows them to permit virtually any employer or college to opt out of providing contraceptive coverage entirely, including for reasons as amorphous as vaguely designed moral beliefs.”

In addition to the Trump administration, a charity called Little Sisters of the Poor defended the rules. The order of nuns, which runs homes for the elderly and employs about 2,700 people, points out that the government provided exemptions from the beginning for religious organizations such as churches. They say the accommodation provision violates the 1993 Religious Freedom Restoration Act, the law that says the government must have a compelling reason for programs that substantially burden religious beliefs.

In 2014, Alito wrote for the majority in Burwell v. Hobby Lobby that certain closely held businesses do not have to offer birth control coverage that conflicts with the owners’ religious beliefs. But the court did not take a position on the accommodation provision, which requires objecting organizations to notify the government.

Two years later, a shorthanded court of eight justices declined to rule on the merits of another challenge to the contraceptive-coverage requirement and sent the case back to the lower courts. The unusual, unsigned decision was viewed as a punt by the court then equally divided along ideological lines.

The third day of oral argument via teleconference went smoothly Wednesday even as Ginsburg participated from Johns Hopkins Hospital in Maryland, where she is recovering from treatment of a gallbladder condition. The one exception came during the day’s second argument in a free-speech case over unwanted telemarketing calls. About an hour into the discussion, the distinct sound of rushing water — like that of a toilet flush — could be heard in the background.

A court representative did not immediately respond to questions about which justice or lawyer had forgotten to mute his or her phone line.

The combined cases are Trump v. Pennsylvania and Little Sisters of the Poor v. Pennsylvania.

Robert Barnes contributed to this report.