WASHINGTON — The Supreme Court weighed moral theology and parsed insurance terminology Wednesday in an extended and animated argument that seemed to leave the justices sharply divided over what the government may do to require employers to provide free insurance coverage for contraception to female workers.

A 4-4 tie appeared to be a real possibility, which would automatically affirm the four appeals court decisions under review.

All four ruled that religious groups seeking to opt out of the requirement that they pay for the coverage must sign forms and provide information that would shift the cost to insurance companies and the government. A tie vote in the Supreme Court would not set a national precedent, and religious groups in different parts of the country would have conflicting obligations for what they must do if they object to covering contraception.

Other appeals courts have also agreed that the accommodation offered to religious groups is lawful. But the Eighth US Circuit Court of Appeals, which hears cases from federal courts in Arkansas, Iowa, Minnesota, Missouri, Nebraska, North Dakota, and South Dakota, ruled that it violated the Religious Freedom Restoration Act of 1993.

Wednesday’s case grew out of a regulation requiring many employers to provide the coverage for contraception under the Affordable Care Act. Religious institutions such as schools and churches have said that forcing them to comply with that violates the religious freedom law. They also objected to an alternative offered by the government that would allow them to opt out of the requirement by completing a form.

The court’s four more liberal members appeared ready to endorse that alternative.

“There has to be an accommodation,’’ Justice Ruth Bader Ginsburg said. “And that’s what the government tried to do.’’

But it appeared unlikely that the liberal justices would be able to attract the crucial vote of Justice Anthony M. Kennedy, who repeatedly questioned whether the accommodation was making the groups “complicit in the moral wrong’’ by hijacking their insurance plans.

Though Justice Clarence Thomas asked no questions, there was little doubt about where the three more conservative justices stood. Justice Samuel A. Alito Jr., for instance, citing arguments in supporting briefs, said the government’s approach represented “an unprecedented threat to religious liberty in this country.’’

Much of the argument concerned whether the government could provide free contraception coverage without using the groups’ insurance plans.

Alito suggested, for instance, that the government could use the insurance exchanges created under the Affordable Care Act.

The burden on women would be minimal, Alito said. “So she’ll have two insurance cards instead of one,’’ he said.

But Justice Sonia Sotomayor said it was important to make obtaining coverage easy.