WASHINGTON — A seemingly divided Supreme Court is exploring a possible compromise ruling in the dispute between faith-based groups and the Obama administration over birth control.

The justices issued an unusual order Tuesday directing both sides in the case that was argued last week to file a new round of legal briefs. They're asked to examine the minimum the groups must do in order to register their objection to paying for contraception. The Obama administration wants to ensure that women covered under the groups' health plans have access to cost-free birth control.

The court set an April 20 deadline, suggesting that the justices want to resolve the case by late June. A 4-4 tie would leave different rules in place in different parts of the country because lower courts have issued conflicting rulings.

Another option is to leave the issue unsettled until a ninth justice takes the place of Justice Antonin Scalia.

The administration devised what it has called a generous moral and financial buffer to spare the not-for-profit colleges, charities and advocacy groups from any involvement in the provision of contraceptives to which they object on religious grounds. But the groups complain that they remain complicit in the process because they have to object to the contraceptive coverage by notifying the government or their insurer. The groups say the process triggers the government's hijacking of their health plans — a description Chief Justice John Roberts and Justice Anthony Kennedy also used during last week's arguments.

In the order Tuesday, the court asked both sides to discuss whether contraceptive coverage could be provided without the groups having to object at all. The court even suggested a way this could happen.

The nonprofit groups could tell their insurance company at the time they arrange for health insurance that they don't want to include some or all contraceptive coverage, the court said. Armed with that knowledge, the insurer would notify people covered by the health plan that contraceptive coverage would come directly from the insurer, with no money from or involvement by the nonprofit's health plan.

Mark Rienzi, a lawyer for the groups, called the order “an excellent development.”

Rienzi said it shows the court recognizes that “the government's current scheme forces them to violate their religion.”

Contraception is among a range of preventive services that must be provided at no extra charge under the 2010 health care overhaul.