Eric C. Rassbach, a deputy general counsel of the Becket Fund, said the relief offered by the government was not a complete exemption. By signing the form, he said, the nuns would be “designating someone else to provide the contraceptive drugs and devices” to which they object.

“It makes them complicit,” Mr. Rassbach said. The nuns do not want to sign the form because it would “authorize and designate” the administrators of their health plan, including Express Scripts, to provide contraceptives, he said.

“The Little Sisters and other applicants cannot execute the form because they cannot deputize a third party to sin on their behalf,” the nuns said in a reply brief filed Friday six hours after the government filed. The nuns said that they “face ruinous fines for their religious refusal to sign the forms,” and that this threat was a substantial burden on their exercise of religion.

However, the Obama administration said Friday that it could not compel Christian Brothers Services to provide contraceptive coverage to employees of the Little Sisters nursing homes. In any event, it said, the Christian Brothers company does not intend to provide such coverage.

Moreover, the Obama administration said that the Affordable Care Act did not really impose an “employer mandate.”

The birth control requirements “apply only if an employer offers a group health plan,” the administration said in its brief.

“Employers, however, are not required to offer group health plans in the first place,” the brief continued. “Large employers (those with more than 50 full-time-equivalent employees) face a potential tax if they do not provide coverage, but that gives them a choice between two legal options: provide a group health plan or risk payment of the tax.”