President Obama, seeking to dampen a runaway political furor over birth control and religious liberty, unveiled a plan on Friday that is meant to calm the right's ire about a new administration rule that would require health insurance plans - including those offered by Roman Catholic hospitals, universities and charities - to provide free birth control to female employees.

Casting himself as both "a citizen and a Christian" trying to balance individual liberty versus public health, Mr. Obama announced what administration officials called an "accommodation" that they said sought to demonstrate respect for religious beliefs. It will be similar to the path taken in several other states - particularly Hawaii - that have similar rules, but would require that insurance companies, and not religious institutions, offer contraceptive coverage at no cost.

"Religious liberty will be protected, and a law that requires free preventive care will not discriminate against women," Mr. Obama told reporters in the White House briefing room. He said the "political football" his foes were making of the new rule prompted him to speed up work on a solution. "It became clear that spending months hammering a solution was not going to be an option."

But administration officials also acknowledged that the revision announced Friday would most likely fail to mollify the Catholic bishops who have waged war against the rule or, for that matter, Republicans in Congress and on the presidential campaign trail who have joined the fight. At most, the compromise could potentially help the president shore up support among wavering Democrats, who have also expressed doubt about the rule, along with more liberal religious organizations and charities, who oppose the rule but not as vehemently as the Catholic leadership.

In a statement, Archbishop Timothy M. Dolan of New York, the president of the United States Conference of Catholic Bishops, called the move a "step in the right direction," but said the bishops would reserve judgment on the plan until they had the details.

The administration plan most closely resembles Hawaii's, in which employees at religious institutions whose health insurance plans do not offer free contraception can get birth control through side benefits. The difference, though, is that whereas in Hawaii the employees nominally pay for the benefits, the Obama proposal would shift the cost to insurers. Administration officials hope that insurers will not object because in the long run, they argue, contraceptives end up saving more money than they cost because they prevent unwanted pregnancies.

The administration's move won an important endorsement from Sister Carol Keehan, president and chief executive officer of the Catholic Health Association of the United States, whose support the White House sees as essential to show that the policy is backed by some religious organizations. In fact, Sister Carol's endorsement was so important that Mr. Obama called her Friday morning - along with Archbishop Timothy M. Dolan of New York and Cecile Richards, the president of Planned Parenthood - to inform her of the compromise.
"The Catholic Health Association is very pleased with the White House announcement that a resolution has been reached that protects the religious liberty and conscience rights of Catholic institutions," Sister Carol said in a statement. "The framework developed has responded to the issues we identified that needed to be fixed."

Abortion rights groups also seemed open to the White House shift and blamed the controversy on conservative efforts to undermine the president.

"We're reassured that it appears that no woman, no matter where she works, will lose birth control coverage, but it's outrageous and disheartening that this important step forward for women became a target of the far-right," said Stephanie Schriock, president of Emily's List.

Nancy Keenan, president of Naral Pro-Choice America, said the Obama administration's action represented a reaffirmation of the commitment to ensuring contraceptive coverage. "Unfortunately, some opponents of contraception may not be satisfied," she said.

The administration announced the birth-control rule last month, and since then, Republican presidential candidates and conservative leaders have sought to frame it as an example of the administration's insensitivity to religious beliefs, prompting Mr. Obama's aides to explore ways to make it more palatable to religious-affiliated institutions, perhaps by allowing some employers to make side insurance plans available that are not directly paid for by the institutions.