Cardinal Timothy Dolan, Archbishop of New York, said that while he understands why a South Carolina priest chose to withhold Communion from former Vice President Joseph R. Biden over his stance on abortion, he would not have done so himself.

“I think that priest had a good point,” Cardinal Dolan told Fox News on Oct. 31. “You are publicly at odds with an issue of substance, critical substance. We’re talking about life and death in the church. You personally, out of integrity, should not approach Holy Communion, because that implies that you’re in union with all the church beliefs.”

Cardinal Dolan added that he has never denied anyone Communion, but he noted that he has held private conversations with public officials about their political stances.

“My job is to help people make, with clear Church teaching, make a decision on the state of their soul and the repercussions of that,” the cardinal said.

Cardinal Timothy Dolan: “If only saints could receive Holy Communion, we wouldn’t have anybody at Mass, including myself.”

He said he “admires” Catholics who refrain from taking Communion if they do not agree with church teaching on important issues. But he also pointed to Pope Francis and his approach to the Eucharist.

“We also remember Pope Francis: ‘I personally can never judge the state of a person’s soul.’ So, it’s difficult, that’s what I’m saying. I’m not there as a tribunal, as a judge in distributing Holy Communion,” the cardinal said.

“If only saints could receive Holy Communion, we wouldn’t have anybody at Mass, including myself,” he added.

Mr. Biden attended Mass at St. Anthony Catholic Church in Florence, S.C. on Oct. 27, and when he presented himself to receive the Eucharist he was refused by the pastor. Father Robert Morey wrote in a statement responding to queries from the Florence Morning News that he “had to refuse holy Communion” to Mr. Biden because a “public figure who advocates for abortion places himself or herself outside of church teaching.”

Mr. Biden, campaigning in his 2020 bid for president, was in South Carolina Oct. 26-27 attending a town hall meeting in Florence and a justice forum in Columbia. He frequently references his Catholic faith and when at home he attends Mass at St. Joseph on the Brandywine in Greenville, Del.

The Diocese of Wilmington, Mr. Biden’s home diocese, released a statement saying that the Bishop William Francis Malooly “has consistently refrained from politicizing the Eucharist, and will continue to do so. His preference, as with most bishops, is to interact with politicians individually who disagree with significant church teachings.”

While Mr. Biden has not spoken in depth about the incident, he did address the controversy earlier this week.

Asked about it Tuesday on MSNBC, the former longtime Delaware senator shifted to an overall discussion of his views on faith.

“I practice my faith,” Biden told the network. “But I’ve never let my religious beliefs, which I accept based on church doctrine… impose that view on other people.”

A number of his supporters have defended him. A progressive faith-based political group called Faithful America created a petition condemning the episode.

Edward Peters, a professor of canon law, invoked church law to explain that Mr. Biden’s private views on abortion do not outweigh his public position.

“Holy Communion is not a tool for punishing political opponents. We have seen this despicable behavior before, used by right-wing clergy to attack John Kerry and Tim Kaine,” the petition reads, referring to two other high-profile Catholics who were nominated for the presidency and vice presidency, respectively, by the Democratic Party. Each of those men also faced questions about their eligibility for Communion.

Some Catholics have said the priest was correct in denying Mr. Biden Communion. Edward Peters, a professor of canon law at Sacred Heart Major Seminary in Detroit, invoked church law to explain that Mr. Biden’s private views on abortion do not outweigh his public position. He wrote in The Hill that the priest was correct to deny Communion.

“To confuse the private examination of one’s conscience as envisioned by Canon 916 with the recognition that some public acts warrant public consequences under Canon 915 is to show either ignorance of or indifference to well-established Catholic pastoral and sacramental practice,” he wrote.

But Charles Camosy, a theologian at Fordham University and author of Beyond the Abortion Wars, took to Twitter to say that the cardinal’s view was correct.

“Biden has moved away a nuanced position [on abortion], and thus created a plausible case for his being denied communion. The same case, however, if applied apolitically, would be made for lots and LOTS of other people being denied,” Mr. Camosy wrote. “Dolan was correct to resist the false choice between either artificially giving preference to one part of the Gospel or going to war with virtually all public Catholic figures in NYC.”

Material from Catholic News Service and the Associated Press was used in this report.

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.