President Barack Obama today announced his administration would no longer require religiously affiliated hospitals and institutions to provide employees with insurance plans that include contraception services and took a hard shot at critics that have turned the rule into a political controversy.

The changes to the rule, which will exempt not only churches but also hospitals, charities and other institutions related to religious orders, come after 10 days of escalating attacks from Republicans and the leadership of the Catholic Church.

“I understand that some folks in Washington may want to treat this as another political wedge issue. But it shouldn’t be,” Obama said, taking aim at Congressional Republicans who have seized on the controversy as evidence of the administration’s war on religion.

Obama defended the rule, arguing that, “We fought for this because it saves lives and it saves money. … That’s because it’s a lot cheaper to prevent an illness than to treat one.”

“We know the overall cost of health care is lower when women have access to contraceptive services,” the president added.

According to Obama, the new rule will still ensure that “whether you’re a teacher or a small-business woman or a nurse or a janitor, no woman’s health should depend on who she is, where she works or how much money she makes” while ensuring Catholic and other religious institutions — which regard contraception as a sin — are not “directly providing contraception services to their employees.”

Originally, Obama said he wanted “to spend the next year working … to find an equitable solution that protects religious liberty and ensures that every woman has access to the care she needs.”

But “after the many genuine concerns that have been raised over the last few weeks, as well as, frankly, the more cynical desire on the part of some to make this a political football, it became clear that spending months hammering a solution was not going to be an option,” Obama explained, adding that, “Last week, I directed the Department of Health and Human Services to speed up the process.”

Although the White House saw supporters of abortion rights and women’s organizations quickly come out to back the changes, Republicans remained critical.

House Republican Study Committee Chairman Jim Jordan (Ohio) today panned the changes, saying in a statement that the rule “still tramples on Americans’ First Amendment right to freedom of religion. It’s a fig leaf, not a compromise. Whether they are affiliated with a church or not, employers will still be forced to pay an insurance company for coverage that includes abortion-inducing drugs.”

Other critics, however, did seem to find the changes acceptable.

For instance, Carol Keehan, CEO of the Catholic Health Association of the United States, said in a statement that her organization was pleased with the modifications.

“We are pleased and grateful that the religious liberty and conscience protection needs of so many ministries that serve our country were appreciated enough that an early resolution of this issue was accomplished. The unity of Catholic organizations in addressing this concern was a sign of its importance,” Keehan said.

The CHA had been a significant supporter of Obama’s health care reform law, and its opposition to the original contraceptive rule was a major political blow.

Sen. Barbara Boxer (D-Calif.), a supporter of the original rule, praised the announcement.

“The president has made clear that we can — and must — protect women’s health and the religious freedom of all. The fact that groups from Planned Parenthood to the Catholic Health Association support this policy should put an end to the vicious political attacks and allow us all to focus on providing these critical health benefits to millions of American women and families,” she said.