A leading Democrat wants pro-life Americans to know they are welcome in the party, hoping to end weeks of debate about whether support for abortion rights is a litmus test for party support.

“I grew up Nancy D’Alesandro, in Baltimore, Maryland; in Little Italy; in a very devout Catholic family; fiercely patriotic; proud of our town and heritage, and staunchly Democratic,” House Minority Leader Nancy Pelosi told the Washington Post in an interview published Tuesday. “Most of those people—my family, extended family—are not pro-choice. You think I’m kicking them out of the Democratic Party?”

Her comments follow a wave of criticism from pro-life Democrats after Tom Perez, chair of the Democratic National Committee, made comments implying that Democratic candidates who do not support abortion rights would not be eligible for support from the party. “I won’t let anyone get in the way of our fight to protect a woman’s right to choose,” said Mr. Perez in a statement on April 20.

Most of those people—my family, extended family—are not pro-choice. You think I’m kicking them out of the Democratic Party?

Ms. Pelosi, an ardent supporter of abortion rights and a practicing Catholic, suggested that it was not the case that pro-life Democratic candidates were unwelcome in the party. But she also expressed skepticism that a Democrat opposed to abortion would make it very far in the political process.

“Can somebody get the nomination? I don’t think so,” she said. “I don’t think that you’ll see too many candidates going out there and saying, ‘I’m running as a pro-life candidate.’”

She also suggested that controversy about abortion, at least in the Democratic Party, is “kind of fading as an issue.” She implied that most Democrats who describe themselves as pro-life do not want abortion to be outlawed, but disagree about how far along in a woman’s pregnancy the procedure should be allowed.

An April 2016 poll from the Pew Research Center found that most Americans, 56 percent, said abortion should be legal in all or most cases. Broken down by party, most Democrats say abortion should be legal, though 28 percent said it should be illegal in all or most cases. But another poll from November found that 18 percent of Democrats believed the same.

Ms. Pelosi conceded that while most candidates seeking support from the party would support abortion rights, “It depends on where [in the United States] you are talking about.”

That’s an important concession, one that cuts to the genesis of the controversy.

Last month, Vermont Senator Bernie Sanders and Keith Ellison, a Minnesota congressman and deputy chairman of the Democratic National Committee, campaigned for Heath Mello, a Democrat trying to unseat the Republican mayor of Omaha. Some pro-choice leaders took issue with the endorsement, citing Mr. Mello’s past support for legislation advocated by some pro-life activists.

Following Mr. Sanders’s campaign event for Mr. Mello, Ilyse Hogue, the head of NARAL Pro-Choice America, said in a statement that the event was “not only disappointing, it is politically stupid.”

That prompted Mr. Perez, head of the D.N.C., to say in a statement that every Democrat “should support a woman’s right to make her own choices about her body and her health,” dubbing that position “not negotiable.”

Even some of the nation’s top bishops weighed in on the party’s internal dispute. Cardinal Timothy Dolan of New York called Mr. Perez’ statements “very disturbing” and “intolerant,” while Philadelphia’s Archbishop Charles Chaput interpreted them as “celebrating” killing.

In her interview with the Post, Ms. Pelosi suggested the only litmus test for Democratic candidates is support for working families.

“In our caucus, one thing unifies us: our values about working families,” she said. “Some people are more or less enthusiastic about this issue or that issue or that issue. They’ll go along with the program, but their enthusiasm is about America’s working families.”

Ms. Pelosi’s comments echo those made by other Democrats in recent days, who seemed to bristle at Mr. Perez’s idea that pro-lifers were excommunicated from the party.

“I couldn’t disagree more with what Tom Perez said, I think it’s not correct that our party should have litmus tests about who wants to join our party,” Senator Claire McCaskill of Missouri, who supports abortion rights, told the Atlantic on April 27. “We may disagree on various issues, and I just don’t think we should say ever anyone is not welcome in our party based on one of those issues.”

The head of the Democratic Party in Arkansas also recoiled at the notion that pro-life Americans were not welcome in the party.

“The only litmus test we care to take is whether what we do is in the best interest of the people we serve,” Rep. Michael John Gray told the Arkansas Democrat-Gazette. “Ideological purity leaves little room for compromise on our most important issues.”

Ms. Pelosi, meanwhile, appeared to lay blame at the hands of pro-life Catholics and Evangelicals for President Trump’s surprise victory in November, suggesting that those voters overlooked their other concerns such as immigration and climate change.

“You know what? That’s why Donald Trump is president of the United States—the evangelicals and the Catholics, anti-marriage equality, anti-choice. That’s how he got to be president,” she said. “Everything was trumped, literally and figuratively by that.”

Still, she recalled with fondness her work with Catholic sisters in the United States to help pass the Affordable Care Act in 2010. Their support, cited as instrumental in helping pass the law, came over objections from U.S. bishops, who are today urging Republicans not to repeal the law without guaranteeing Americans will be able to retain health insurance.

“The Catholic nuns,” Ms. Pelosi said, “thank God for the Catholic nuns.”

Michael J. O’Loughlin is national correspondent at America and author of Hidden Mercy: AIDS, Catholics, and the Untold Stories of Compassion in the Face of Fear.