Several conservative and religious groups applauded the new standards, which they said would protect health providers from being compelled to provide services that conflicted with their beliefs.

“Quite frankly, it’s a horrible, awful thing, regardless of what your personal beliefs are about abortions, that a nurse like Cathy DeCarlo was forced to participate in one, despite the fact that she is pro-life,” said Melanie Israel, a research associate at the Heritage Foundation. She was referring to a complaint that a nurse successfully lodged against a New York hospital in 2013. Mr. Severino mentioned the same case in his remarks on Thursday.

Ms. Israel said the Trump administration’s actions on religious and conscience exemptions had been important not just because of strengthened enforcement, but also because they had brought attention to the issue.

Mr. Severino said complaints made to his office had increased sharply. The Obama administration averaged just over one per year. By contrast, the office has received 343 complaints in the last fiscal year alone, Mr. Severino said.

A series of civil rights laws has long protected health care workers from offering certain types of care that conflict with their religious beliefs. But the new regulation pulls together 25 separate laws — some dealing only with abortion services, some with advance directives, and many that had typically not been overseen by the department’s Office for Civil Rights — into one broad framework. It also protects workers who not only decline to provide care but also refuse to refer patients to someone who will provide it.

“The goal of the proposed rule was to expand the universe of individuals and conduct that would be protected under the provider conscience laws, and to institute a broader range of enforcement tools and formal requirements,” said Jocelyn Samuels, who was the director of the office for civil rights for part of the Obama administration, and is now the executive director of the Williams Institute at the University of California, Los Angeles. She expressed concern that the rule could affect women’s access to reproductive health care, and care for L.G.B.T. patients more generally.

Laws written in the 1970s to provide protections to workers who objected to sterilization procedures, for example, are cited in the rule. The old laws were brought up in connection with recent cases about health care workers with religious objections to treating transgender patients.