The White House has lost perhaps its most prominent Catholic ally in its controversial effort to expand contraception coverage, with the huge Catholic Health Association saying Friday that the mandate for most religious employers to offer coverage would not “adequately meet the religious liberty concerns.”

The change of position at the association, the country’s largest group of nonprofit health-care providers, comes as polls show President Obama and Mitt Romney tied among registered Catholic voters. For the past four of five presidential races, the candidate who won Catholics won the presidency.

In a five-page letter to the Department of Health and Human Services, leaders of the association said the group supports Obama’s overall health-care overhaul but thinks he should broaden the exemption for religious groups that say facilitating the use of contraception in any way goes against their beliefs.

The mandate that employers, including most religious ones, offer employees a variety of preventive services, including contraception, without any out-of-pocket charge, has been controversial among some from the start, particularly Catholic bishops. Actual houses of worship were exempted, but not faith-based institutions such as schools and hospitals that don’t primarily employ or serve people of the same faith.

The White House this year attempted to allay the concerns of faith-based employers by announcing that such employers wouldn’t have to pay directly for the contraception coverage. Instead, health insurers would pay at no additional cost to the employers. But opponents, most visibly the bishops, said that still violated their faith and conscience.

In contrast, the health association, led by Sister Carol Keehan and made up of more than 2,000 health-care entities, said it was comfortable with the compromise. But Friday’s letter includes the same concerns the bishops have voiced all along: that the mandate codifies in law that houses of worship are inherently “religious” — and thus entitled to an exemption — but that faith-based social service groups aren’t.

The mandate as is “parses a bona fide religious organization into secular and religious components solely to impose burdens on the secular portion. To make this distinction is to create a false dichotomy between the Catholic Church and the ministries through which the Church lives out the teachings of Jesus Christ. Catholic health care providers are participants in the healing ministry of Jesus,” the letter said.