Amid a backlash from many Catholics and proponents of religious liberty, President Barack Obama announced Friday that his administration will not require religious institutions like hospitals and universities to provide free contraception to their employees in their health insurance.

Speaking to reporters at the White House Friday, Obama offered a compromise that would allow women to obtain free contraception but would require them to obtain it directly from their insurance companies if their employers object to birth control because of religious beliefs.

"Whether you're a teacher or a small businesswoman or a nurse or a janitor, no woman's 's health should depend on who she is, or where she works, or how much money she makes," Obama said, calling free contraceptive care a "core principle" of his health care law, which requires that all preventive services be provided at no cost to patients.

Obama went out of his way to say that he supports freedom of religion, pointing out that one of his stints as a community organizer in Chicago was funded by a Catholic group.

"As a citizen and as a Christian I cherish this right," Obama said. "I saw that local churches did more good for a community than a government program ever could."

Planned Parenthood and the Catholic Health Association each approved of the compromise, which the White House is calling an "accommodation," in statements on Friday.

Obama's staff was deeply divided over the decision to require free contraception, with Vice President Joe Biden and Defense Secretary Leon Panetta, both Catholics, very opposed, ABC's Jake Tapper reported earlier this week.

White House officials said on a conference call with reporters Friday that the proposal would allow the government to guarantee preventive services to "nurses, teachers, janitors, mothers" who work at religious organizations, while maintaining "religious liberties."

When pressed, the White House officials--who asked to remain anonymous--did not say they are confident that the proposal will end objections from Catholic bishops. Cardinal-designate Timothy Dolan, the head of the United States Conference of Catholic Bishops, said in a statement Friday afternoon that Obama's announcement is "a first step in the right direction," but that he does not know all of the details yet. "We hope to work with the Administration to guarantee that Americans' consciences and our religious freedom are not harmed by these regulations," he said.

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The Obama administration says insurers can provide birth control for free because contraception reduces costs for them overall by preventing expensive-to-cover pregnancies, as well as reducing the risk of ovarian cancer.

Some are skeptical of Obama's claim that insurers won't pass on their costs to religious employers. "If you believe the insurance companies will actually provide the drugs for free, you know nothing of economics," Red State blogger Erick Erickson wrote on Twitter. Sarah Kliff at the Washington Post points to a Guttmacher Institute report that estimates it costs about $21 per patient to add contraception to a plan for a year. Even if those costs were offset by a reduction in pregnancies as the Obama administration suggests, the up-front cost to insurance companies would be considerable.

Holly Bailey and Liz Goodwin contributed reporting.

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