Sen. Kirsten Gillibrand on Thursday vowed to “codify” Roe v. Wade if elected president, amid a fierce abortion debate in the wake of Alabama’s new state law banning almost all abortion procedures.

During a visit to Atlanta Thursday, the 2020 Democratic presidential hopeful touted her “robust reproductive rights agenda,” and promised to take her plans a “step further.”

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“First, as president, I will codify Roe v. Wade. I will make it clear beyond a shadow of a doubt that women in this country have a guaranteed right to an abortion,” Gillibrand, D-N.Y., said.

“Second, I will end the Hyde Amendment, which disproportionately blocks women of color and women with low incomes from getting access to abortion services,” she continued. “And third, in the most sweeping step that I’m going to take as president, I will guarantee access to reproductive health care, including abortion, no matter what state you live in.”

Gillibrand added that she would create a “funding stream” to make sure that women have access to reproductive health centers in every state.

“I would ensure that no state can pass laws that chip away at access to reproductive care or criminalize reproductive health care providers,” she explained. “Federal law should supersede harmful state laws that take away women’s reproductive freedom.”

Gillibrand said that she believed that access to abortion is a “constitutionally recognized right.”

“I’m not afraid to follow through and guarantee it,” she said. “With the power of the federal government, this is about the fundamental question of whether we value women in this country and whether we see them as humans who are able to make their own decision.”

She added: “And any Democrat who expects to win the presidency must answer definitively where they stand on this issue.”

Gillibrand’s comments come amid a heated national debate over Alabama’s new state law, which bans nearly all abortion procedures.

Alabama Gov. Kay Ivey, a Republican, signed the bill into law Wednesday. The law makes nearly all abortions in the state illegal and makes performing one a felony, punishable by up to 99 years or life in prison unless the mother’s health is at risk, with no exceptions for women impregnated by rape or incest.

Republican state Rep. Terri Collins, who sponsored the bill, aimed to reignite the debate surrounding Roe v. Wade, the 1973 Supreme Court decision that legalized abortions across the nation, and to push justices to overturn the landmark ruling.

Currently, the law will not be enforceable because of the current Supreme Court ruling that makes abortions a constitutional right. Ivey acknowledged this when she signed the bill into law.

"In all meaningful respects, this bill closely resembles an abortion ban that has been a part of Alabama law for well over 100 years. As today’s bill itself recognizes, that longstanding abortion law has been rendered unenforceable as a result of the U.S. Supreme Court decision in Roe v. Wade,” she said.

"No matter one’s personal view on abortion, we can all recognize that, at least for the short term, this bill may similarly be unenforceable. As citizens of this great country, we must always respect the authority of the U.S. Supreme Court even when we disagree with their decisions,” she continued.

“Many Americans, myself included, disagreed when Roe v. Wade was handed down in 1973. The sponsors of this bill believe that it is time, once again, for the U.S. Supreme Court to revisit this important matter, and they believe this act may bring about the best opportunity for this to occur."

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A Fox News poll conducted in February tallied voters' familiarity with Roe v. Wade, and 48 percent said they are “extremely” or “very” familiar with the ruling while the exact same number are “somewhat” or “not at all” familiar with the case.

Moreover, 57 percent of voters say the Supreme Court should let the 46-year old ruling stand; that number jumps to 68 percent among those who are familiar with the case.

Meanwhile, on Capitol Hill on Thursday, House Republican Leader Kevin McCarthy, R-Calif., said the Alabama law “goes further than I believe.”

McCarthy said he believed in “exceptions for rape, incest and life of the mother,” but wouldn’t go as far as to take a stand on whether the Supreme Court should strike down the Alabama law if it were to reach the high court.

But Alabama is not the only state in the nation with an abortion law as restrictive as the one passed this week. In March, Mississippi's Republican Gov. Phil Bryant signed a bill that outlaws most abortion procedures once a fetal heartbeat can be detected. The law makes it illegal for a woman to have an abortion after approximately six weeks of pregnancy.

At the time, the Center for Reproductive Rights called the bill “blatantly unconstitutional,” and has threatened to sue the state to block the law from going into effect on July 1.

“The term ‘heartbeat bill’ is a manipulative misnomer. These bills actually rob women of their choice to have an #abortion before they even know they’re pregnant,” the group tweeted in March.

Also in Ohio, the legislature proposed a similar measure during former Gov. John Kasich’s term. Kasich vetoed the proposal, but the new Republican governor, Mike DeWine, has indicated he will support the bill. The measure passed the Ohio Senate last week.

Kentucky passed a similar bill last month, and Iowa Gov. Kim Reynolds, last spring signed a 'heartbeat' bill into law.

Meanwhile, states like New York, Virginia, New Mexico, Massachusetts, Rhode Island and Washington have either passed new laws expanding abortion access, or are moving toward stripping old laws from the books that limit abortions.

In New York, non-doctors are now allowed to conduct abortions and the procedure can be done until the mother's due date if the woman's health is endangered or if the fetus is not viable. The previous law only allowed abortions after 24 weeks of pregnancy if a woman's life was at risk.

Fox News’ Ben Florence, Vandana Rambaran, Victoria Balara, and The Associated Press contributed to this report.