WASHINGTON - Under fierce election-year fire, President Barack Obama on Friday abruptly abandoned his stand that religious organizations must pay for birth control for workers, scrambling to end a furor raging from the Catholic Church to Congress to his re-election foes. He demanded that insurance companies step in to provide the coverage instead.

Obama's compromise means ultimately that women would still get birth control without having to pay for it, no matter where they work. The president insisted he had stuck by that driving principle even in switching his approach, and the White House vehemently rejected any characterization that Obama had retreated under pressure.

Yet there was no doubt that Obama had found himself in an untenable position. He needed to walk back fast and find another route to his goal.

The controversy over contraception and religious liberty was overshadowing his agenda, threatening to alienate key voters and giving ammunition to the Republicans running for his job. It was a mess that knocked the White House off its message and vision for a second term.

Leaders from opposite sides of the divisive debate said they supported the outcome - or at least suggested they probably could live with it. Cardinal-designate Timothy Dolan of New York, the head of the nation's Roman Catholic bishops and a fierce critic of the original rule covering hospitals and other employers, said the bishops were reserving judgment but that Obama's move was a good first step.

The bishops' organization later issued a far more skeptical critique contending that the new approach offered insufficient protections for religious employers and calling that unacceptable.

Republicans hoping to oust Obama from the White House were conceding nothing. Though not mentioning the birth control issue, Newt Gingrich assailed the president's views of religious rights and said "I frankly don't care what deal he tries to cut. ... If he wins re-election, he will wage war on the Catholic Church the morning after he's re-elected."

Mitt Romney, the front-runner in the campaign for the GOP presidential nomination, said the decision didn't change anything.

"Today he did the classic Obama retreat, all right, and what I mean by that is it wasn't a retreat at all. It's another deception," Romney said while campaigning in Portland, Maine.

Obama, acknowledging he wanted a resolution to the controversy, ordered advisers to find a middle ground in days, not within a year as had been the plan before the uproar. He said he spoke as a Christian who cherishes religious freedom and as a president unwilling to give up on free contraceptive care.

"I've been confident from the start that we could work out a sensible approach here, just as I promised," Obama said. "I understand some folks in Washington may want to treat this as another political wedge issue, but it shouldn't be. I certainly never saw it that way."

Under the new plan, religious employers such as charities, universities and hospitals will not have to offer contraception and will not have to refer their employees to places that provide it. If an employer opts out of the requirement, its insurance company must provide birth control for free in a separate arrangement with workers who want it.

"Very pleased," was how Sister Carol Keehan, president of the Catholic Health Association, reacted in a statement distributed by the White House. Her trade group represents Catholic hospitals that had fought against the birth control requirement, and Keehan said the new arrangement addresses the concerns it had.

In searching for a way out of the crisis, Obama also had to be mindful not to anger many women and fellow Democrats.

Planned Parenthood, a prominent women's health organization, said Obama had reaffirmed his commitment to birth control coverage. The group's president, Cecile Richards, added, though, that it would be monitoring for "rigorous, fair and consistent" enforcement so women get the promised coverage.

Before announcing his decision to reporters, Obama telephoned Keehan, Richards and Dolan.

At the Conservative Political Action Conference in Washington, where Gingrich made his comments, many said the White House rewrite did not change anything.

"It's an accounting trick," said Mike Gonzales of the Heritage Foundation. "Do they think people are stupid?"

The debate within the White House was intense even before the Jan. 20 decision was announced to exempt only churches and other houses of worships from the requirement that employers must cover free contraception. Other religious organizations were given an extra year to comply, but that concession didn't do enough.

First in a rumble, and then in a roar, critics formed a movement to overturn what they considered to be an egregious violation. Bishops assailed the policy in Sunday Masses and Republican leaders in Congress pledged to push a legislative repeal.

The White House seemed to be caught flatfooted.

"The past three weeks have witnessed a remarkable unity of Americans from all religions, or none at all, worried about the erosion of religious freedom and government intrusion into issues of faith and morals," said Dolan, the president of the United States Conference of Catholic Bishops.

The turmoil, in turn, prompted advocates from other sides to get vocal in the battle for public opinion. They defended the rights of women and the need for preventive health care, including contraception, to be provided without fee for people of all faiths, no matter where they work.

Officials said Obama has the power under his health law to compel insurance companies to provide free contraception coverage directly to workers.

The health insurance industry voiced concern that putting the burden on them could set a precedent of shifting cost its way. The insurance companies will weigh in later as Obama's new policy undergoes review, said Robert Zirkelbach, spokesman for the America's Health Insurance Plans trade group.

Administration officials say providing birth control won't cost insurers any more in the long run, because it's less expensive than the costs of maternal care and delivery. But insurers say they'll have to pay drug companies for pills and doctors for prescriptions, so it won't be free to them. The costs probably will be passed on to policyholders, as is happening already with other requirements of the health care law, such as allowing young adults to stay under their parents' coverage until age 26.

By keeping free contraception for employers at religious workplaces - but providing a different way to do it - Obama was able to assert he had found "a solution that works for everyone." Unclear was why the White House had not come up with the idea in the first place.

While Obama in 2008 won the total Catholic vote, 54 percent to Sen. John McCain's 45 percent, he lost the white Catholic vote, 52 percent to 47 percent, according to exit polls. Once reliably Democratic, Catholics are now swing voters, with white Catholics making up the majority of the group.

The Rev. Joel C. Hunter, a moderate evangelical leader and a spiritual adviser to the president, said he thinks Obama responded quickly enough to heal the rifts with many of his religious allies. "I think it's simple enough that most people will say, 'Oh good, we can get to other things now,"' said Hunter.

Yet the change just led to more criticism from some of Obama's opponents.

A spokesman for House Speaker John Boehner said that that initial response indicated church leaders were not yet convinced the mandate respected religious freedom. Boehner has said he believes the original measure violates First Amendment rights, and his office said Friday that he would seek legislation.

House Minority Leader Nancy Pelosi, D-Calif., an ardent support of the original measure, offered a restrained response. Focusing on the benefits of health care, she said: "I appreciate the president's unifying approach."

Associated Press writers Julie Pace, Erica Werner, Ricardo Alonso-Zaldivar, Jim Kuhnhenn, Laurie Kellman, Rachel Zoll, Jay Lindsay and Steve Peoples contributed to this report.