U.S. Catholic bishops on Thursday debated whether to lay out standards for denying Communion to politicians including President Biden who support abortion rights, a question that has split the U.S. Catholic hierarchy and raised tensions with Pope Francis.

The bishops were considering a proposed doctrinal document on the Eucharist that would include a section on the conditions under which Catholic politicians may receive Communion. The bishops voted on the proposal Thursday, with results to be announced Friday.

The issue has become a proxy for disagreements among bishops about which agenda to give priority to in their dealings with U.S. political leaders: traditional moral and cultural values or social and economic justice. The debate also reflects bishops’ different views over the leadership of Pope Francis, who has played down abortion as a political issue by comparison with his predecessors.

“Almost daily I speak with people, Catholics, laity, who are confused by the fact that we have a president who professes devout Catholicism and yet advances the most radical pro-abortion agenda in our history,” Bishop Donald Hying of Madison, Wisconsin, said at the spring meeting of the United States Conference of Catholic Bishops. “They’re looking for some direction, some teaching from us.”

But Cardinal Joseph Tobin of Newark, N.J., and one of Pope Francis’s closest allies among the U.S. bishops, warned, “Any effort by this conference to move in support of the categorical exclusion of Catholic political leaders from the Eucharist based on their public-policy positions would thrust the bishops of our nation into the very heart of the toxic partisan strife which has distorted our own political culture and crippled meaningful dialogue.”

President Biden arrived for Mass at Holy Trinity Catholic Church in Washington earlier this month.

President Biden arrived for Mass at Holy Trinity Catholic Church in Washington earlier this month.

PHOTO: ERIN SCOTT/REUTERS

The two were among more than three dozen bishops who spoke on the matter on the second day of the USCCB meeting. Only a few of the bishops explicitly mentioned Mr. Biden or House Speaker Nancy Pelosi, both Catholics who support abortion rights.

ADVERTISEMENT - SCROLL TO CONTINUE

That section of the proposed document addressing Catholic politicians was originally proposed in December by a committee formed to deal with the Biden administration. Some bishops have wanted that section to state that politicians such as Mr. Biden who support abortion rights are ineligible to receive the sacrament. The Vatican has discouraged such a move, warning that it could be divisive, and the pope himself has signaled his preference for a more conciliatory approach to the Biden administration.

On Wednesday, the head of the bishops’ doctrinal committee announced that it had modified its proposal for the document on Communion in deference to Vatican concerns.

“We are no longer proposing a national policy” on politicians receiving Communion, said Bishop Kevin Rhoades of Fort Wayne-South Bend, Ind. He said the final doctrinal document might still include practical guidance for bishops dealing with Catholic politicians who support abortion rights.

The White House didn’t comment on the Thursday debate. White House spokesman Andrew Bates has said in the past that Mr. Biden is a “strong person of faith.”

President Joe Biden at St. Joseph on the Brandywine Roman Catholic Church in Wilmington, Del., last month.

President Joe Biden at St. Joseph on the Brandywine Roman Catholic Church in Wilmington, Del., last month.

PHOTO: KEN CEDENO/REUTERS

Disagreement over how to deal with Mr. Biden has divided the Catholic hierarchy from the start of the administration. On inauguration day in January, Archbishop José Gomez of Los Angeles, who is president of the USCCB, wrote that “our new President has pledged to pursue certain policies that would advance moral evils,” including abortion and contraception. Cardinal Blase Cupich of Chicago tweeted an extraordinary public rebuke of Archbishop Gómez.

ADVERTISEMENT - SCROLL TO CONTINUE

By contrast, a public statement by Pope Francis on the same day didn’t mention or allude to the new president’s deviations from Catholic teaching. In November, the pope departed from custom to phone Mr. Biden to congratulate him on his election win.

Mr. Biden is a frequent Mass-goer who regularly receives Communion. Cardinal Wilton Gregory, who as archbishop of Washington is the president’s pastor, has said that he wouldn’t deny Mr. Biden the sacrament.

Pope Francis has often denounced abortion. However, he made clear early in his pontificate that he would play down the issue in favor of questions of social and economic justice, including inequality, the rights of migrants and protection of the environment.

“Inevitably this debate is also a referendum on Pope Francis because those bishops who feel we need to take an exceptionally strong line on Biden because of abortion, they don’t feel supported by this pope,” said John Allen, president of Crux Catholic Media and author of numerous books on the church.

SHARE YOUR THOUGHTS

Should Catholic politicians who support abortion rights be able to receive Communion? Join the conversation below.

The Vatican’s approach to pro-abortion-rights Catholic politicians has shifted markedly since 2004, when then- Sen. John Kerry, a Catholic who supported abortion rights, was the Democratic nominee for president. Then-Cardinal Joseph Ratzinger, later Pope Benedict XVI, instructed U.S. bishops that a Catholic politician who actively supported legalized abortion should be denied Communion.

ADVERTISEMENT - SCROLL TO CONTINUE

Cardinal Ratzinger also wrote that “not all moral issues have the same moral weight as abortion and euthanasia…There may be a legitimate diversity of opinion even among Catholics about waging war and applying the death penalty, but not however with regard to abortion and euthanasia.”

By contrast, his successor as Vatican doctrinal chief, Cardinal Luis Ladaria, warned the U.S. bishops last month that “it would be misleading if such a statement [on Communion] were to give the impression that abortion and euthanasia alone constitute the only grave matters of Catholic moral and social teaching that demand the fullest level of accountability on the part of Catholics.”

Write to Francis X. Rocca at francis.rocca@wsj.com