(Reuters) - President Barack Obama, in an abrupt policy shift aimed at quelling an election-year firestorm, announced on Friday that religious employers would not be required to offer free birth control to workers and the onus would instead be put on insurers.

But Catholic Church leaders and Obama's Republican opponents, who had railed against the Democratic president's new rule on contraceptives as a violation of religious freedom, signaled that divisions remain over the hot-button social issue.

The compromise by the Obama administration sought to accommodate religious organizations, such as Catholic hospitals and universities, outraged by a new rule that would have required them to offer free contraceptive coverage to women employees.

Instead, the new approach puts the burden on insurance companies, ordering them to provide workers at religious-affiliated institutions with free family planning if they request it, without involving their employer at all, the White House said.

"Religious liberty will be protected, and a law that requires free preventive care will not discriminate against women," Obama told reporters in the White House briefing room as he sought to put the political furor to rest.

The U.S. Conference of Catholic Bishops called Obama's move a "first step in the right direction" but said it was still concerned about the issue and would reserve judgment.

Weighing in publicly on the issue for the first time, Obama acknowledged that religious groups had "genuine concerns" about the birth control rule, but he accused some of his opponents of a cynical effort to turn the issue into a "political football."

"The result will be that religious organizations won't have to pay for these services," Obama said. "But women who work at these institutions will have access to free contraceptives just like other women."

The rule had sparked an outcry not only from Catholic leaders but from social conservatives, including Republican presidential hopefuls on the campaign trail, and had also sown dissent among some of Obama's top advisers.

Health insurance giant Aetna Inc said it would comply with the policy but needed "to study the mechanics of this unprecedented decision before we can understand how it will be implemented and how it will impact our customers."

Republicans seized on the issue, seeing a chance to paint Obama as anti-religion and put him on the defensive as signs of economic recovery appear to have re-energized his re-election bid.

The policy shift was aimed at preventing the issue from becoming a liability for Obama with Catholic voters, while at the same time trying not to anger his liberal base.