WASHINGTON—After intense criticism, the Obama administration on Friday said nonprofit affiliates of religious organizations, such as hospitals and universities, will not be required to offer prescription contraceptive drug coverage to their employees.

Under the new policy, full coverage—with no copayments or other cost-sharing requirements—would have to be offered by the employers' health insurers. The insurer could not charge a premium for the coverage.

A senior administration official said extending the coverage would be cost neutral to insurers due to a reduction in number of pregnancies.

In regulations issued Friday, the administration said it will be developing a comparable rule that would apply to employers affiliated with religious organizations that self-fund their health care plans.

The administration says it intends “to develop policies to achieve the same goals for self-insured group health plans sponsored by non-exempted, non-profit organizations with religious objections to contraceptive coverage.”

The new requirement would apply for plan years that begin on or after Aug. 1. 2013.

The new rule contrasts sharply with one the administration released last month. Under that rule—mandated by the health care reform law—employers would have had to include the prescription contraceptive drug coverage directly in their group policies.

But that rule triggered a huge and growing wave of criticism from religious organizations and lawmakers from both sides of the aisle.

This week, Speaker of the House John Boehner, R-Ohio, said he would work to get legislation passed to block the rule, drawing support from some Democrats as well.

“If the president does not reverse the…attack on religious freedom, then the Congress, acting on behalf of the American people and the Constitution we are sworn to uphold and defend, must” act, Speaker Boehner said on the House floor.

The change in policy does not affect other parts of the prescription contraceptive drug rule.

The requirement to offer full coverage will apply to other employers for plan years that begin on or after Aug. 1, 2012.

However, the mandate would not apply to religious organizations, such as churches, that primarily employ those who share in their beliefs, and to employers with grandfathered health care plans.