Planned Parenthood said all of its clinics will formally leave Title X, the marquee federal program dedicated to providing birth control to low-income women. A change to the program last year requires beneficiaries to comply with a so-called "gag order" on abortion services — something that Planned Parenthood said it isn't willing to do. The clinic's exit will result in a loss of millions of federal dollars.

In a conference call with reporters on Monday, Planned Parenthood's new leader, Alexis McGill Johnson, announced all the health care clinic's affiliates would be sending letters to the Department of Health and Human Services Monday, formally announcing their resignation from Title X. She warned that without Planned Parenthood, low-income women in rural areas would struggle to find affordable birth control options.

"For too many people struggling to make ends meet, it may be that they may go without care," Johnson said on the call.

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Planned Parenthood leadership declined to answer exactly how much revenue the organization would lose due to the exit. "Our position is that this isn't about Planned Parenthood's budget, it's about our patients," Johnson said.

Title X was created in 1970 to provide affordable reproductive care to women who otherwise couldn't afford it. Last year, more than four million people relied on Title X for health care services, 41% of whom received services at Planned Parenthood, according to the health clinic.

Title X funds have never been authorized to pay for abortions. Instead, the money is used for wellness exams, STD and HIV screenings, birth control and contraceptive education, according to Planned Parenthood.

But in February, a 312-page filing from the Department of Health and Human Services proposed what abortion rights advocates have referred to as a "gag rule." Under the proposal, the agency wrote that "none of the funds appropriated for Title X may be used in programs where abortion is a method of family planning." The changes impact not just Planned Parenthood, but any clinic that supports, performs or even refers patients for abortion services.

Under the new rule, recipients of Title X funds can reference abortion as an option to pregnant women, but they are not allowed to refer them to an abortion provider.

Mia Heck, a senior adviser at the Department of Health and Human Services, said in a statement emailed to CBS News on Monday afternoon that Title X recipients shouldn't have accepted the funds if the organizations were uncomfortable with the so-called "gag rule."

"Some grantees are now blaming the government for their own actions - having chosen to accept the grant while failing to comply with the regulations that accompany it - and they are abandoning their obligations to serve their patients under the program," Heck said.

In an exclusive interview with CBS News in July, Johnson said that the organization would be fighting the changes in court — and was confident that they would win.

"We believe it is really critically important to stand up with our patients," said Johnson, acting president and chief executive officer of Planned Parenthood Federation of America and the Planned Parenthood Action Fund. "We are identifying all strategies — all hands on deck — to try to identify the best strategies in order to make sure we can sustain and keep our doors open for our patients no matter what."

Anti-abortion rights advocates argue that any money given to Planned Parenthood — even if it's not used for abortions — frees up funding to be used for the procedure.

"Abortion is neither healthcare nor family planning and taxpayer dollars should not support abortion," said Jeanne Mancini, President of the March for Life, in a statement emailed to CBS News on Monday afternoon. "Leana Wen's recent firing and Planned Parenthood's decision today doubles down on their ultimate goal, which is political abortion advocacy, not healthcare."