The Republican battle against the President Obama's new birth-control mandate will continue until the policy is reversed, the top GOP senator warned Sunday.

Senate Minority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump, GOP aim to complete reshaping of federal judiciary Supreme Court fight should drive Democrats and help Biden Harris on SCOTUS fight: Ginsburg's legacy 'at stake' MORE said Obama's rule requiring employer-based healthcare plans – even those sponsored by faith-based groups – to cover contraception infringes on the religious freedoms guaranteed by the Constitution. The Kentucky Republican vowed to fight the policy until the White House "backs down."

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"In this country the government doesn't get to tell you or your organization what your religious views are – and they could well be minority views – but the Bill of Rights is designed to protect the minority from the will of the majority," McConnell said on CBS's "Face the Nation."

"So this issue will not go away until the administration simply backs down. They don't have the authority … to tell someone in this country, or some organization in this country, what their religious beliefs are. Therein lies the problem."

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Obama on Friday outlined his plan to guarantee female workers – even those employed by Catholic hospitals, universities and charities – free access to birth control. Critics had attacked an earlier version of that plan because it required employers to cover the cost. In an effort to allay those concerns, Obama shifted the cost burden of the contraceptives from the objecting employer to the employer's insurance company.

Making the rounds on the Sunday shows, White House Chief of Staff Jack Lew Jacob (Jack) Joseph LewApple just saved billion in tax — but can the tax system be saved? Lobbying World Russian sanctions will boomerang MORE said the policy threads the needle between protecting religious freedom and ensuring women have access to comprehensive healthcare services. Lew said those were Obama's goals all along.

"His position was, is and has been that women have a right to a full range of preventative health, including contraception, and you have to do it in a way that's respectful of religious differences," he told "Face the Nation."

In a post at the White House blog the administration touted the support of numerous groups including Catholic Charities, Planned Parenthood and NARAL Pro-Choice America.

White House Deputy Communications Director Jennifer Palmieri said the policy had "earned praise from a wide range of individuals and organizations."

But while the policy was welcomed by Democrats and women's healthcare groups – including some Catholic affiliates – it was panned by Republicans and the US Conference of Catholic Bishops, which want the mandate rescinded.

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The outcry, McConnell charged, just "underscores" the constitutional problems with the Democrats' healthcare reform law, which was the source of the new policy. On Monday, Senate Republicans will file an amicus brief in the Supreme Court case against the healthcare law, McConnell said.

Behind Sen. Roy Blunt Roy Dean BluntGOP senators confident Trump pick to be confirmed by November Sunday shows preview: Lawmakers prepare for SCOTUS confirmation hearings before election SCOTUS confirmation in the last month of a close election? Ugly MORE (R-Mo.), some Republicans want not only to repeal the mandate on faith-based non-profits, but to extend waivers to any group or person who objects to the coverage requirements for either religious or moral reasons.

McConnell said he'd "be happy to support" legislation repealing the mandate, but didn't seem to endorse the Blunt bill specifically.

"We'll be voting on that [repeal] in the Senate, and you can anticipate that that will happen as soon as possible," he said.

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This story was updated at 4:34 p.m.