President Obama said Friday that he will require insurance companies to offer free birth control to women employed by religious organizations that have objections to paying for and providing contraceptive services. 

"We fought for this because it saves lives and it saves money," Obama said from the White House briefing room. "No woman's health should depend on who she is or where she works or how much money she makes."

Obama's announcement alters a proposal he made three weeks ago, in which he said all employers except churches and houses of worship must provide free birth control. Republican lawmakers and some religious leaders blasted the proposal as an attack on religious liberty. 

Under the new rule, other religiously-affiliated organizations are also exempt from offering contraception coverage.

"If a woman's employer is a charity or a hospital that has a religious objection to providing contraceptive services as part of their health plan, the insurance company ... will be required to reach out and offer the woman contraceptive care free of charge, without co-pays and without hassles."

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Referring to Republican lawmakers' objection to his original proposal, Obama said, "Some in Washington may want to treat this as another political wedge issue, but it shouldn't be, and I certainly never saw it that way."

He accused his critics of have a "cynical desire" to turn the issue into "political football."

He said he respects the separation of church and state, and "As a citizen and as Christian, I cherish [religious liberty]."