President Biden denounced on Friday new restrictions on abortion imposed in Republican-led states in the year since the Supreme Court overturned Roe v. Wade and warned that the right to privacy, which has been the foundation for other rights like same-sex marriage and access to birth control, could be at risk next if Democrats do not win next year’s elections.

Marking Saturday’s anniversary of the Dobbs v. Jackson Women’s Health Organization decision eliminating a national right to abortion for women, Mr. Biden decried its “devastating effects,” telling an abortion rights rally that women had been deprived of basic health care and noting that some leading Republicans, not content to leave the issue to the states as they had long advocated, are now seeking a national ban on the procedure.

“They’re not stopping here,” said Mr. Biden, who was joined at the rally by his wife, Jill Biden, as well as Vice President Kamala Harris and her husband, Doug Emhoff. “Make no mistake, this election is about freedom on the ballot.”

The president collected the endorsement of the nation’s leading abortion rights groups, Emily’s List, Planned Parenthood Action Fund and NARAL Pro-Choice America. While the endorsement was hardly a surprise, the early timing underscored the role that Democrats believe abortion rights will play in next year’s election.

Polls show that support for legalized abortion has risen since the Dobbs decision. Democrats argue that it helped them avoid a Republican wave during last year’s midterm elections — “you all showed up and beat the hell out of them,” as Mr. Biden put it — and could be critical to retaining the White House and recapturing the House next year. Republicans are at odds with each other over how much to emphasize the issue, with some worried that it will only hurt them in a general election. But some progressive activists have privately expressed frustration that Mr. Biden has not made it more of a public priority until now.

Abortion has long been an uncomfortable issue for Mr. Biden, who has cited his Catholic faith as his views have shifted over the years. While a young senator, he declared that the Supreme Court had gone “too far” in the Roe decision and later voted for a constitutional amendment allowing states to individually overturn the ruling before reversing himself. He supported the so-called Hyde amendment prohibiting the use of federal funds for abortion, including through Medicaid, until the 2020 campaign, when he changed his mind under pressure from liberals in his party.

By contrast, Ms. Harris has unabashedly joined the battle for abortion rights since Roe was reversed, becoming by all accounts the administration’s most passionate and effective voice on the issue. At Friday’s event, Laphonza Butler, president of Emily’s List, praised Mr. Biden’s team as “the most pro-choice administration we’ve ever seen” but reserved her most effusive words for Ms. Harris.

The rally on Friday, organized with the Democratic National Committee, was part of a series of messaging efforts by the Biden team around the anniversary of the Dobbs ruling. Earlier this week, Dr. Biden hosted a session with women from states that have imposed limits on abortion to highlight the consequences even for those not seeking to end a pregnancy. On Saturday, Ms. Harris will deliver an address on abortion rights in Charlotte, N.C.

Mr. Biden’s allies on Capitol Hill on Friday also called attention to the issue. House Democrats led by Representative Ayanna S. Pressley of Massachusetts introduced legislation to require insurance coverage to include abortion care, shield patients and providers from criminal charges, and affirm a legal right to abortion and miscarriage care. The bill has no chance of passing the Republican-controlled House but was meant as a signal to supporters.

As he has over the last year, Mr. Biden sought to expand the debate to other privacy-related concerns, ideological ground where he is more comfortable, as he cast Republicans as extremists beyond the question of abortion. The White House announced Friday that in his third executive action in response to the Dobbs decision, he was ordering federal agencies to look for ways to ensure and expand access to birth control.

“The idea that I had to do that — I mean, no, really, think about it, think about it,” he told supporters. “I know I’m 198 years old but all kidding aside, think about that. I never, ever thought I’d be signing an executive order protecting the right to contraceptives.”

He boasted that he had done more to put women in positions of power than any of his predecessors. In addition to making Ms. Harris the first woman to serve as vice president, he noted that he is the first president to have a majority-woman cabinet, pointed to his appointment of Ketanji Brown Jackson as the first Black woman on the Supreme Court and said that he had installed more Black women to federal appeals courts than all of the previous presidents combined.

“Look, we made so much progress,” Mr. Biden said. “We can’t let them take us backwards.”