WASHINGTON — Federal officials, following through on a pledge by President Trump, have drafted a rule to roll back a federal requirement that many religious employers provide birth control coverage in health insurance plans.

The mandate for free contraceptive coverage was one of the most hotly contested Obama administration policies adopted under the Affordable Care Act, and it generated scores of lawsuits by employers that had religious objections to it.

On its website, the White House Office of Management and Budget said it is reviewing an “interim final rule” to relax the requirement, a step that would all but ensure a court challenge by women’s rights groups.

Mr. Trump signaled a change in direction on May 4, when he issued an executive order instructing three cabinet departments to consider amended regulations to “address conscience-based objections to the preventive-care mandate.” The order cites a section of the Affordable Care Act that refers specifically to preventive services for women.