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The battle over the Obama administration's contraceptive coverage rule is far from over despite the "accommodation" announced Friday, as the U.S. Conference of Catholic Bishops and other groups voice serious concern about a policy they claim still intrudes on religious freedom.

President Obama announced the rule change in a bid to calm the tumultuous debate which had spread to the Republican presidential campaign trail and beyond. The original policy would exempt churches and house of worship but require religious organizations like schools and hospitals to provide free contraceptive coverage. Under the change, religious organizations could refuse that coverage, while insurers would nevertheless be required to offer it to any employee who wants it.

The change was initially met with a reserved response. While many Democrats praised it and Republicans dismissed it, nonpartisan groups like the Conference of Catholic Bishops said they were reserving judgment.

But the Conference, after earlier calling the change a "first step in the right direction," issued a lengthy statement overnight blasting the plan. And they joined others in calling for legislation in Congress to reverse the policy, something Republicans said they were not abandoning despite Friday's announcement.

"We think there needs to be a legislative fix to protect our religious liberties," Bishop William Lori, a member of the Conference, told Fox News on Saturday. "I think that our First Amendment religious rights are far too precious to be entrusted to regulatory rules."

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    Lori and the rest of the Conference said they want to see the "mandate" rescinded altogether. They pointed out several lingering concerns. They said the change appears to make no consideration for religious insurers or self-insuring religious employers -- or for religious for-profit employers and secular nonprofit employers.

    The statement from the Conference, more broadly, expressed concern that the requirement would still facilitate contraceptive coverage even if an employer objects to it.

    "And in the case where the employee and insurer agree to add the objectionable coverage, that coverage is still provided as a part of the objecting employer's plan, financed in the same way as the rest of the coverage offered by the objecting employer. This, too, raises serious moral concerns," the statement said.

    The Conference went on: "But stepping away from the particulars, we note that today's proposal continues to involve needless government intrusion in the internal governance of religious institutions, and to threaten government coercion of religious people and groups to violate their most deeply held convictions. ... The only complete solution to this religious liberty problem is for HHS to rescind the mandate of these objectionable services."

    A spokesman for House Speaker John Boehner said the religious community is "not yet convinced" the revised rule is not an "attack on religious freedom," and said the House would continue to work toward a "legislative solution."

    More than three-dozen religious scholars and leaders of different faiths also put out a statement Friday afternoon calling the change "unacceptable." Professors and officials from the University of Notre Dame, Harvard University and other institutions argued that the shift "changes nothing of moral substance," since it still "coerces" religious groups to offer policies that will, regardless of whether the groups are paying for it, offer contraceptive coverage.

    But Obama said the issue should not be treated as a "political wedge."

    "Under the rule, women will still have access to free preventive care that includes contraceptive services, no matter where they work -- that core principle remains," Obama said. But he added, "Religious organizations won't have to pay for these services, and no religious institution will have to provide these services directly."

    The administration circulated statements of support Friday from both Planned Parenthood and the Catholic Health Association of the United States.

    Former Virginia Gov. Tim Kaine, a Democrat who had been critical of the original plan, also praised the change.

    "There are some who have wrongly used this debate to pit women's rights against freedom of religion. The steps taken by the White House show that there is a way to respect both," Kaine said in a statement. "The significant increase in access to contraception under the Affordable Care Act is an important step forward. I believe that access to contraception and health care is critical to reducing unintended pregnancies and abortions."