WASHINGTON—Two Orthodox groups protested the Obama administration’s decision to amend regulations that would require faith-based groups to cover “religiously objectionable medical services.”

Agudath Israel of America on Wednesday and the Union of Orthodox Congregations on Tuesday released statements criticizing the action taken Jan. 20 by the Department of Health and Human Services.

As part of the Affordable Care Act, employer-provided health insurance plans are required to include contraception and related “preventive” services for employees, but there is an exemption in the law for houses of worship and other religious institutions.

Both Agudath Israel and the Orthodox Union were hoping the administration would expand the exemption for other religious organizations that do not necessarily fall into the category of houses of worship.

Agudah noted in its statement that the decision “only muddied the waters and took a step backwards by imposing religiously objectionable mandates on religious entities and by devising an astoundingly counterproductive limitation on what ‘religious groups’ are and what their public mission in society should be.”

Nathan Diament, executive director of the Orthodox Union, emphasized in a statement that the “most troubling” aspect of the decision was the Obama administration’s “underlying rationale for its decision, which appears to be a view that if a religious entity is not insular, but engaged with broader society, it loses its ‘religious’ character and liberties.”