WASHINGTON — House Speaker John Boehner accused the Obama administration today of an “unambiguous attack on religious freedom,” promising that Congress will reverse a new policy requiring religious schools and hospitals to provide employees with free birth control if the president doesn’t.

Escalating a fight that has roiled the presidential race, Boehner demanded that President Barack Obama overturn the policy that Boehner called a violation of First Amendment rights. The administration’s mandate has angered religious groups, especially Catholics, who say the requirement would force them to violate their beliefs against contraception, and congressional Republicans.

“This attack by the federal government on religious freedom in our country cannot stand, and will not stand,” Boehner, a Catholic and Ohio Republican, said in a rare floor speech.

On the other side of the Capitol, the Republican onslaught continued, with GOP senators vowing to push ahead with legislation to undo the requirement.

Sen. Kelly Ayotte, R-N.H., stood with other GOP lawmakers, and called the new rule “an unprecedented affront to religious liberty. This is not a women’s’ rights issue. This is a religious liberty issue.”

Said Sen. Marco Rubio, R-Fla.: “This has nothing to do with contraception. …. This is about whether the government of the United States should have the power to go in and tell a faith-based organization that they have to pay for something that they teach their members shouldn’t be done. It’s that simple. And if the answer is yes, then this government can reach all kinds of other absurd results.”

The White House, facing a public and political outcry, signaled on Tuesday that a compromise is possible. Options could include granting leeway for a church-affiliated employer not to cover birth control, provided it referred employees to an insurer who would provide the coverage.

Another idea, previously rejected by the administration, calls for broadening the definition of a religious employer that would be exempt from the mandate beyond houses of worship and institutions whose primary purpose is to spread the faith. That broader approach would track a definition currently used by the IRS, bringing in schools, hospitals and social service agencies that deal with the general public.

Republican White House hopefuls Mitt Romney and Newt Gingrich have been relentless in assailing the administration, criticizing the president at campaign stops. Romney has accused Obama of an “assault on religion” and Gingrich called the rule an “attack on the Catholic Church.”

Boehner said that if the administration fails to reverse the policy, then Congress will act. He said that in the coming days, the House Energy and Commerce Committee will move ahead on legislation.