President Obama on Wednesday marked the 41st anniversary of the Roe v. Wade decision with a statement calling on the nation to "recommit" to the principle "that every woman should be able to make her own choices about her body and her health."

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"We reaffirm our steadfast commitment to protecting a woman’s access to safe, affordable health care and her constitutional right to privacy, including the right to reproductive freedom," Obama said.

"And we resolve to reduce the number of unintended pregnancies, support maternal and child health, and continue to build safe and healthy communities for all our children. Because this is a country where everyone deserves the same freedom and opportunities to fulfill their dreams."

The president's statement comes amid a broader battle over abortion rights looming over this year's election cycle. In 2012, Democrats highlighted Republican candidates' opposition to abortion, as well as controversial comments made about rape, to accuse the GOP of waging a "war on women."

But some Republicans said this week that they will look to highlight Democratic positions on abortion rights as part of their electoral strategy.

On Tuesday, CNN reported some members of the GOP plan to introduce a resolution at this week's meeting of the Republican National Committee encouraging Republican candidates to discuss abortion openly.

"The Republican National Committee urges all Republican pro-life candidates, consultants, and other national Republican Political Action Committees to reject a strategy of silence on the abortion issue when candidates are attacked with 'war on women' rhetoric," the resolution reads.

Rep. Tom Cotton Tom Bryant CottonRenewed focus on Trump's Supreme Court list after Ginsburg's death Republicans call for DOJ to prosecute Netflix executives for releasing 'Cuties' Loeffler calls for hearing in wake of Netflix's 'Cuties' MORE (R-Ark.) also noted the anniversary in a fundraising email to supporters on Wednesday.

"I am proud to have fought (and will continue fighting) for pro-life legislation in Congress. However, like most of the legislation my fellow conservative House members and I pass, the U.S. Senate blocks those bills from becoming law," Cotton, who is challenging Sen. Mark Pryor Mark Lunsford PryorCoronavirus poses risks for Trump in 2020 Tom Cotton's only Democratic rival quits race in Arkansas Medicaid rollback looms for GOP senators in 2020 MORE (D-Ark), wrote. "This is just another reason we need to take back the Senate from Harry Reid Harry Mason ReidSenate Republicans signal openness to working with Biden Mellman: The likely voter sham Bottom line MORE and President Obama's other close allies."

— Cameron Joseph contributed.