Former Vice President Joseph R. Biden Jr., who has shunned today’s Democratic Party orthodoxy on issues from crime to compromising with Republicans, again broke with his party’s base and many of his campaign rivals on Wednesday when his campaign confirmed that he still backs the Hyde Amendment, a measure that prohibits the use of federal funds for abortion with exceptions for cases involving rape, incest and when the life of the mother is in danger.

The backlash to Mr. Biden, who despite leading early presidential polls faces skepticism from his party’s progressive wing, came swiftly from lawmakers and activists who support abortion rights, with many noting that the Hyde Amendment disproportionately affects economically disadvantaged women and women of color.

“The problem is, the Hyde Amendment affects poor women, women of color, black women, Hispanic women,” said Patti Solis Doyle, who served as Hillary Clinton’s presidential campaign manager in 2008 and has also worked for Mr. Biden. “And women of color will elect the next president of the United States.”

Several of Mr. Biden’s primary opponents moved quickly Wednesday to highlight their own opposition to the Hyde Amendment, underscoring how sharply Mr. Biden’s position differs from many in the Democratic field. The measure, which dates back to the 1970s, pertains to Medicaid funding of abortion, which is why opponents say the restrictions impact poor women most directly.

“Repealing the Hyde Amendment is critical so that low-income women in particular can have access to the reproductive care they need and deserve,” Senator Kirsten Gillibrand of New York tweeted. “Reproductive rights are human rights, period. They should be nonnegotiable for all Democrats.”

Senator Bernie Sanders of Vermont took a thinly veiled swipe as well. “There is #NoMiddleGround on women’s rights,” Mr. Sanders wrote. “Abortion is a constitutional right. Under my Medicare for All plan, we will repeal the Hyde Amendment.”

Speaking with reporters after a rally in Indiana, Senator Elizabeth Warren of Massachusetts emphasized her opposition to the measure.

“This isn’t about politics, this is about what’s right,” she said. “The Hyde Amendment should not be American law.”

Mr. Biden’s current position on the issue was first reported by NBC News and confirmed by his campaign. It is at odds with the current Democratic Party platform, which calls for a repeal of the Hyde Amendment.

In a statement, Planned Parenthood Action Fund cast his view as out of step with the rest of his party.

“The Democratic Party platform is crystal clear in supporting the right to safe, legal abortion and repealing the Hyde Amendment, a position held by the majority of voters,” said Kelley Robinson, the executive director of the organization. “We strongly encourage Joe Biden to speak to the people whose lives are impacted by this discriminatory policy and reevaluate his position.”

[Inside the battle between Ms. Warren and Mr. Sanders, two of Mr. Biden’s rivals, for liberal voters and donors.]

The scrutiny of Mr. Biden’s position comes as numerous states have moved to enact far-reaching restrictions on abortion.

“There’s no political or ideological excuse for Joe Biden’s support for the Hyde Amendment, which translates into discrimination against poor women and women of color,” said Ilyse Hogue, president of the abortion rights organization Naral Pro-Choice America. “Differentiating himself from the field this way will not earn Joe Biden any political points and will bring harm to women who are already most vulnerable.”

News of Mr. Biden’s stance was greeted with shock and disbelief among progressives on Capitol Hill, who have been pushing for the amendment’s repeal on the grounds that it harms poor women who cannot afford abortions.

“You can’t tell me that this vice president who has been a champion for women would want to continue a discriminatory policy that is so detrimental to poor women, to women of color, to low income women,” said Representative Barbara Lee, Democrat of California, who is supporting Ms. Harris in the presidential race. “I didn’t see that, but that’s hard to believe.”

Representative Alexandria Ocasio-Cortez, Democrat of New York, conceded that getting rid of the amendment would be difficult, but said it was important for Democrats to oppose it.

“Politically I can understand that that is a challenge, but I don’t think it should be our stance, our belief, to maintain it,” she said. “I know people who lost a baby at 6 months and they had to choose. That’s not a choice that anybody wants to make. Can you just imagine being in that situation and you can’t afford your health care? What are you going to do — just die?”

The former vice president is a Roman Catholic who has long grappled with his position on abortion and once voted to let states overturn Roe v. Wade, which established the constitutional right to the procedure. His campaign confirmed on Wednesday that Mr. Biden “firmly believes that Roe v. Wade is the law of the land and should not be overturned.”

“Will you commit to abolishing the Hyde Amendment, which hurts poor women and women of color?” the volunteer said.

“Yes,” Mr. Biden responded. “Yes, and by the way, A.C.L.U. member, I got a near-perfect voting record my entire career.”

“I heard you did, but I’m glad you just said you would commit to abolishing the Hyde Amendment,” the volunteer replied.

“No no, right now it has to be — it can’t stay,” Mr. Biden said, before turning to greet another person.

In a statement, his campaign said: “Biden misheard the woman on the ropeline and thought she was referring to the Mexico City rule, which prevents federal aid money from going to organizations overseas that perform abortions. He supports the repeal of the Mexico City rule because it prevents critical aid from going to organizations even if abortion is a very small fraction of the work they are doing. He has not at this point changed his position on the Hyde Amendment.”

The statement went on to say that “given the current draconian attempts to limit access to abortion, if avenues for women to access their protected rights under Roe v. Wade are closed, he would be open to repeal.”

A spokesman for Mr. Biden did not immediately respond when asked why, with state efforts to restrict abortion rights already underway, Mr. Biden was not currently open to repealing the amendment.

Several of Mr. Biden’s opponents in the presidential race have pushed new measures to protect abortion access. Ms. Harris has a plan to require that places with a history of unconstitutionally restricting abortion rights receive federal approval before putting new abortion laws into effect. And Ms. Gillibrand, Ms. Warren and Senator Cory Booker of New Jersey were vocal last month in urging Congress to codify abortion rights, a call Mr. Biden later echoed.

Ms. Solis Doyle warned that Mr. Biden’s position on the Hyde Amendment seemed poised to be a liability in the Democratic primary.

“I’m not sure how sustainable it is for Joe Biden to continue to support the Hyde Amendment,” she said. “Politically, it’s a significant problem for him.”