In an order issued on Wednesday, Sotomayor said two for-profit companies controlled by Oklahoma City billionaire David Green and his family did not qualify for an injunction while they challenge the requirement in court.
Hobby Lobby Stores Inc, an arts and crafts chain with more than 500 stores, and Mardel Inc, a chain of 35 Christian-themed bookstores, said it violated their religious beliefs to require that their group health plans cover treatments that could induce abortions.
They said they face possible fines of $1.3 million a day if they disobey the mandate, which takes effect on January 1.
Sotomayor, who hears emergency appeals from the 10th Circuit, said it was not "indisputably clear" that Hobby Lobby and Mardel deserved an injunction, noting that lower courts have been divided in similar cases on whether temporary relief is proper.
"Even without an injunction pending appeal, the applicants may continue their challenge to the regulations in the lower courts," and following a final judgment ask the Supreme Court at that time to consider their appeal, she said.
Sotomayor did not rule on the merits of the companies' religious-based claims.
Kyle Duncan, general counsel for the nonprofit Becket Fund for Religious Liberty, which represents the chains, did not immediately respond to requests for comment. At least 42 lawsuits have been filed over the issue, the fund has said.
Hobby Lobby and Mardel claimed that the contraceptives provision violated the First Amendment to the U.S. Constitution, as well as the Religious Freedom Restoration Act of 1993.
But on November 19, Oklahoma federal judge Joe Heaton refused to issue a preliminary injunction, saying the chains did not have the same religious rights as Green family members. Then on Thursday, the 10th U.S. Circuit Court of Appeals in Denver refused to issue a injunction during the chains' appeal.
Forbes magazine in September called David Green, 71, the 79th richest American, with a net worth of $4.5 billion.
The case is Hobby Lobby Stores Inc et al v. Sebelius et al, U.S. Supreme Court, No. 12A644.
(Reporting by Jonathan Stempel in New York; Editing by Cynthia Osterman)