The public has 30 days to comment on the proposed rule, after which the department can issue a final version. Many advocates said they would expect a variety of legal challenges if it is enacted.

Luke Goodrich, vice president and senior counsel of the Becket Fund for Religious Liberty, which advocates for the rights of people to express their religious faith, said the order was necessary to better align the religious exemption that exists for federal contractors with the broader exemption for religious organizations that exists under federal civil rights law. Under current law, a religious organization that is not a contractor could refuse to hire workers who do not share certain religious beliefs.

Thousands of companies have federal contracts, for food and information technology services, the provision of furniture and military equipment, and much more.

Holly Hollman, general counsel of the Baptist Joint Committee for Religious Liberty, a group that opposes government-funded religion, said the rule would not override state laws intended to protect certain workers, which are not typically pre-empted by federal rules.

In explaining the purpose of the rule, the Labor Department said some religious organizations had indicated they were hesitant to apply for federal contracts because they were unsure if the existing religious exemption applied to them.

“As people of faith with deeply held religious beliefs are making decisions on whether to participate in federal contracting, they deserve clear understanding of their obligations and protections under the law,” Patrick Pizzella, the acting labor secretary, said in a statement.

But Patricia A. Shiu, who ran the federal office that oversees compliance for federal contractors under President Barack Obama, said no contractors or prospective contractors had expressed such concerns during her more than seven years in the job.