The proposal, proponents say, would be narrowly applied to permit only selected men ordained as deacons to become priests. The gathering, however, stopped short of fully endorsing calls to allow women as deacons, an ecclesiastical position that can preside over some rites, such as witness marriages, but cannot celebrate Mass.

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The bishops instead urged the Vatican to reopen debate on ordaining women as deacons — an appeal quickly backed by Francis.

For the first South American pontiff, the proposals for the ordination of married men are certain to bring fresh strains within the church. Catholic conservatives have been at odds with the Argentine pope over his broad outreach, including to divorced and remarried Catholics.

There is little disagreement over the church’s challenges in the vast Amazon region. Priest shortages are so acute that some Catholics are left effectively on their own. At the same time, evangelical denominations are an increasing force across all of Latin America and siphon off more Catholics each year.

“Many of the ecclesial communities of the Amazonian territory have enormous difficulties in accessing the Eucharist,” the bishops said, citing the celebration of the Mass. “Sometimes it takes not just months but even several years before a priest can return to a community to celebrate the Eucharist.”

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The three-week synod was convened to discuss a broad range of issues facing the Amazon region and South America, including the church’s role in helping preserve the rainforest. But it was the proposals on the priesthood and women’s role in the clergy that drew the most attention.

Backers of opening the priesthood to married deacons say it is imperative to keep the church relevant in the Amazon. Conservative critics assailed the plan as potentially opening the door to the end of celibacy and married priests in other parts of the world facing a similar shortage in priests.

The measure, approved 128 to 41, now goes to Francis, who is expected to decide whether he will follow it by the end of the year.

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If he does, it will address some problems but exacerbate others.

Since Francis succeeded a far more conservative pontiff, Benedict XVI, the Vatican has been increasingly consumed by culture wars between traditionalists and progressives.

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The proposals also come at a time of crisis for the church after decades of abuse scandals and, in Latin America and Africa, added pressure from powerful evangelical movements.

These tensions are particularly acute in Brazil, a country long tethered to the rhythms of Catholic life that is now being reshaped by evangelicalism. Catholics, who once accounted for more than 90 percent of the population, are not expected to be even half of it by 2022, according to recent research.

Evangelicals, meanwhile, are surging. They were a key constituency in the rise of Brazil’s nationalist president, Jair Bolsonaro. A former evangelical bishop, Marcelo Crivella, is the mayor of Rio de Janeiro. And they are poised to represent more than 40 percent of the population in the next 15 years.

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The difficulties facing Catholics are even more urgent in the Amazon.

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Patrícia Cabral, president of a Catholic advocacy organization in Manaus, the capital of Amazonas state, sees it every day working in the Catholic community. Some parishes serve nearly 100 different communities separated by vast distances.

“There are few priests who act in this region,” she said. “Many of the communities are difficult to access and it’s only possible to get there by boat. . . . In some places, the [priest] can only go one time per year.”

But not all Catholic leaders in Brazil, which contains more than 60 percent of the Amazon within its borders, were supportive of the proposal.

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“The problem of the dearth of priests is a problem for the Catholic Church in the whole world, except in some nations. Why this exception for the Amazon?” said Bishop D. José Luis Azcona of the Amazonian state of Para.

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Celibacy in the priesthood has been a central part of Roman Catholic tradition for nearly a millennia, but there are some exceptions. Some married Anglican clergy have become priests after converting to Catholicism. There are also married priests in Eastern Rite churches that are in full communion with Rome.

But the proposal would open the door to married clergy in the mainstream Latin Rite church.

Francis has issued conflicting signals on the idea. He has said he does not want to overhaul the requirement of celibacy, but he has indicated he would consider ordaining married men of proven virtue — known as “viri probati” — in “very far places . . . when there is a pastoral necessity.”

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That language led some Vatican observers to suspect that Saturday’s announcement was only the beginning.

“The possibility to ordain viri probati exists in all countries across the Southern Hemisphere,” said retired bishop Fritz Lobinger, an advocate for married priests.

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