The US Supreme Court is exploring a possible compromise on how the government can provide free insurance coverage for contraception to women working for some religious groups.
Some religiously affiliated institutions, including schools, many of them Catholic, say the mandate under President Barack Obama's signature health care reform violates a federal law protecting religious freedom.
With the death of late conservative Justice Antonin Scalia and Senate Republicans' refusal to vote on a replacement until Obama leaves office next year, the court is now evenly split along ideological lines.
Last week, the court heard oral arguments over seven combined lawsuits.
Federal appeals courts handed down inconsistent rulings when they heard the cases -- all but one ruled for the Obama administration -- so a tie would leave a messy patchwork of regulations across the United States.
With that in mind, the court on Tuesday asked the parties to offer new briefs on potential paths to compromise -- particularly on how female employees could get contraception coverage under "Obamacare" from religious employers' health insurance companies, but without direct employer involvement.
Under the health care law, most employers are required to have birth control coverage in their health plans, without forcing workers to pay for them personally.
The four liberal justices have been vocal in their criticism of Christian groups' challenge to the health care reform, formally known as the Affordable Care Act.
Organizations can opt out of the mandate by providing written notification of their opposition on religious grounds. Among the plaintiffs are the Little Sisters of the Poor, a Catholic charity in Washington.
Religious non-profits say the government's accommodation still burdens their free exercise of religion by making them complicit in providing contraception that is contrary to their beliefs.
The court asked the parties Tuesday to provide their supplemental briefs in writing by April 12.
When it agreed in November to hear the case, the Supreme Court denied part of the challenge to the Obamacare contraception mandate, narrowing its focus on whether the mandate violates the Religious Freedom Restoration Act.
Under the 1993 federal law, the government cannot "substantially burden" the free exercise of religion unless it is the least restrictive means to advance the government's interest.
In a landmark 2014 decision in a similar case, the Supreme Court ruled 5-4 that closely held, for-profit corporations -- including arts and crafts retailer Hobby Lobby -- can deny contraceptive coverage to employees for religious reasons.
A decision in the latest case, Zubik versus Burwell, is not expected until June.