The Supreme Court, seemingly split in a case involving contraception coverage, issued an unusual order asking both sides to review a possible compromise. (J. Scott Applewhite/AP)

The Obama administration said a compromise floated by the Supreme Court to resolve objections from religious organizations to providing their employees with contraceptives would work only if it was clear that the women would receive the coverage through other means, and if it ended the controversy.

Solicitor General Donald B. Verrilli Jr. told the court that requiring a modification to the accommodation already offered to the religiously affiliated colleges, charities and hospitals was unnecessary.

He said a modification would be acceptable only if the court ruled that it would satisfy the Religious Freedom Restoration Act and if it halted lawsuits from groups that say providing contraceptive coverage would make them complicit in sin.

Anything less, he wrote, “would lead to years of additional litigation, during which tens of thousands of women would likely continue to be denied the coverage to which they are legally entitled.”

In their brief to the court, lawyers for the groups said they were amenable to a compromise if it truly left the groups out of the process — even having to sign documents that said they objected.

“There are many ways in which the employees . . . could receive cost-free contraceptive coverage through the same insurance company that would not require further involvement by the petitioner, including the way described in the court’s order,” lawyers Paul D. Clement and Noel Francisco wrote.

“And each one of those ways is a less restrictive alternative that dooms the government’s ongoing effort to use the threat of massive penalties to compel petitioners to forsake their sincerely held religious beliefs.”

Clement and Francisco represent, respectively, the Little Sisters of the Poor, a charity run by Catholic nuns, and the Roman Catholic Diocese of Pittsburgh, two of the challengers.

At oral arguments in the case on March 23, the court’s four liberal justices seemed to agree that the Obama administration had offered an acceptable compromise for religiously affiliated organizations that want to be freed from the obligation to supply their female employees with no-cost contraceptive coverage.

The accommodation requires the groups to tell the government they object, then allows the government to work with the groups’ insurers to provide the coverage without the organizations’ involvement or financial support.

But Justice Anthony M. Kennedy, who could provide the fifth vote to uphold such a plan, seemed to agree with the conservative justices that the government would be “hijacking” the groups’ insurance plans to provide the coverage, even if the groups were not paying for it.

Less than a week later, the justices issued an unusual order asking both the government and the groups to provide their reactions to a proposed compromise: Employees could receive contraceptive coverage through their employers’ plans, “but in a way that does not require any involvement” from the employers beyond their decision to provide health insurance.

The difference between that and what the government had already offered, Verrilli said in his new brief, seemed to be only that the groups did not have to certify in writing that they objected to providing the coverage.

But “a requirement that an employer state in writing its religious objection and eligibility for an exemption is a minimally intrusive process, and petitioners have never suggested an alternative arrangement like the one posited in the court’s order,” Verrilli wrote.

The court faces some urgency in trying to find a solution. Eight of the nation’s regional appeals courts have upheld the mandate and the Obama administration’s accommodation, while one has struck them down. Simply reaffirming those decisions would mean that the national health-care law would be enforced differently depending on the location of an organization and its employees.

The court went into unusual specificity in asking the parties to address how that could happen, and it outlined a scenario.

It said an organization could contract to provide health insurance for its employees but inform the insurance company that it did not want the plan to include contraceptive coverage that it found objectionable.

Then the insurer could separately notify employees “that the insurance company will provide cost-free contraceptive coverage, and that such coverage is not paid for by petitioners and is not provided through petitioners’ health plan.”

Under such a plan, the court’s order said, an organization would have no involvement beyond contracting with an insurance provider.

“Petitioners would have no legal obligation to provide such contraceptive coverage, would not pay for such coverage and would not be required to submit any separate notice to their insurer, to the federal government or to their employees,” the order said.

“At the same time, petitioners’ insurance company — aware that petitioners are not providing certain contraceptive coverage on religious grounds — would separately notify petitioners’ employees that the insurance company will provide cost-free contraceptive coverage, and that such coverage is not paid for by petitioners and is not provided through petitioners’ health plan.”

The groups in their response said that to be truly independent, they would essentially “not be complying with that mandate at all. They would be exempt from that mandate, and the commercial insurer would be complying with a separate mandate imposed by the federal government.”

Both sides said an additional compromise would be needed for those organizations that self-insure or contract with a church plan that does not provide contraceptives.

Each side is required to file a brief reacting to the other by April 20. The court will rule before its term ends in June.