WASHINGTON — The Obama administration is announcing a broader opt-out for religious nonprofits that object to providing health insurance that covers birth control.

The administration is allowing religious nonprofits to offer coverage that does not include contraception. In such a case, a third-party issuer will handle all business related to providing birth-control coverage for women, according to a source familiar with the changes who spoke only on condition of anonymity.

Religious groups had said the old birth-control coverage rule violated their religious beliefs. Many filed lawsuits or said they would simply not comply.

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