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 Tuesday directed 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 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 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 is confirmed to take 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 they remain complicit in the process because they have to object to the contraceptive coverage, triggering the government’s hijacking of their health plans.

In the order issued Tuesday, the court asked both sides to discuss whether contraceptive coverage could be provided without the groups having to object.