WASHINGTON — A short-handed Supreme Court dodged but kept alive a legal challenge Monday from faith-based groups over the Obama administration’s rules for cost-free access to birth control. It was the latest sign of justices struggling to find a majority for cases taken up before Justice Antonin Scalia’s death.

The unsigned, unanimous opinion paved a way out of a politically thorny dispute for the eight-member court, which has split twice in 4-4 ties since the conservative jurist’s death in February. Yet it hardly settled the matter, even if President Barack Obama said the “practical effect is right now that women will still continue to be able to get contraception.”

Deciding nothing but perhaps buying time, the justices asked lower courts to take another look at the issue in search of a compromise. The case concerns the administration’s arrangement for sparing faith-based groups from paying the birth control costs of women covered under their health plans.

“The court expresses no view on the merits of the cases,” the justices wrote, ending a major confrontation over Obama’s health care law with a whimper. The matter almost certainly will not return to the Supreme Court before the 2016 presidential election, and perhaps not until a new justice is confirmed to take Scalia’s seat, if at all.

The outcome suggested the court lacked a majority, underscoring the effect of Scalia’s absence. And it pointed to the prospect of other cases ending in a tie among the 31 that remain unresolved.

For now, the government will be able to continue ensuring that women covered by faith-based groups’ health plans have access to cost-free contraceptives. But the groups, which include not-for-profit colleges and charities, won’t face fines for not adhering to administration procedures for objecting to birth control benefits.

Compliance would violate their religious beliefs, the groups argued, because they would be pushing responsibility for providing birth control onto their insurers or insurance administrators.

The administration said the buffer shielded groups from paying for birth control if they objected on moral grounds. It said a ruling for the groups would disadvantage tens of thousands of women.