Sinead O’Connor declaring herself a Catholic priest focuses new attention on the debate over the role of females within the church.

Sinead O’Connor, the 33-year-old Irish pop star, is promoting her new CD, “Faith and Courage,” dressed in a priest’s collar. Though she has been a vociferous critic of the Catholic Church, and famously ripped up the pope’s photograph on “Saturday Night Live” in 1992, she now claims to be an ordained priest.

In a recent interview with Time magazine, she also said she’s changed more than her tune: Her clerical name, O’Connor said, is Mother Bernadette Maria.

Can she really call herself a priest? Not according to the Catholic Church, which does not allow women priests. With her high public profile and outspoken nature, O’Connor has managed to call attention to a brisk and continuing debate about the role of women within the Roman Catholic Church.

“Sinead O’Connor got this idea she’d like to be a priest, a priestess,” said Catholic Press Office spokesman Des Cryan from Dublin, Ireland. “But quite honestly she’s still a pop star and could hardly be assigned a ministry.”

(The clergyman who ordained O’Connor, Bishop Michael Cox, is part of a small renegade sect in Ireland whose own title is not considered valid by the church, according to Cryan.)

The pope let his views be known six years ago when he declared that the church has “no authority to ordain women,” and instructed Catholics to drop the debate.

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Not every Catholic was persuaded. The most recent Gallup Poll shows that 65% of the 770 American Catholics queried favor women priests.

One reason could be the dearth of Catholic men ordained yearly in the U.S. That number fell from 994 in 1965 to 460 last year. (During the same period, the total number of priests in the U.S. dropped from about 58,000 to about 46,000.) And 2,617 Roman Catholic parishes in the U.S. do not have a permanent priest, compared to 549 in 1965. The shortage has led to the rise of “priestless parishes,” managed by nuns or women from the laity. A growing number of parishes also have women on staff who serve as pastoral associates, visit the sick, counsel the grieving and perform other tasks once handled primarily by the parish priest.

“Women are much more visible in leadership roles,” said Deborah Halter of the Women’s Ordination Conference, a 25-year-old advocacy group based in Fairfax, Va. Female parish administrators, she said, do just about everything a pastor does, except administer all seven of the sacraments. “A priest drops in on weekends to give out communion and hear confessions,” she said.

Looking to spark a conversation on the topic, the Women’s Ordination Conference has engaged in a campaign of dueling billboards with the Catholic Archdiocese office in Chicago.

The Archdiocese recruiting office recently put up a billboard that says, “If you’re looking for a sign from God, this is it. Consider the priesthood.”

The Women’s Ordination Conference billboard responds: “You’re waiting for a sign from God? This is it. Ordain women.”

“What the Archdiocese billboard doesn’t say is, ‘Women need not apply,’ ” noted Halter. Her group has 5,000 names on its mailing list. “We decided we should have a billboard too.” A $4,000 budget for the project prompted a fund-raising appeal that brought in $12,000, enough to buy an extra 30 posters to be displayed at train stops around the city.

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The Archdiocese office in Chicago maintains that women’s ordination can’t be discussed on billboards. “The irony,” said Halter, “is that we have no choice. What other way is there? We can’t exactly go into the chancery and have lunch with the bishop to talk about it.”

In the meantime, an underground movement of Catholic women’s groups operates in private homes, conducting ceremonies similar to a Catholic mass without priests. For her 1997 book on the subject, “WomenEucharist” (Wovenword Press), Sheila Durkin Dierks found more than 100 such groups around the country and looked closely at 30 of them.

“These are women who feel impelled to help promote women’s ordination and to supplement their own church life,” she said. Some teach in Catholic schools, oversee religious education programs or are nuns. They would only talk to her anonymously because they feared losing their jobs.

Dierks is part of such a group, which has been meeting for more than five years in Boulder, Colo., where she lives. The women sit in a circle around a table, read from Scripture and refer to God in prayer as “my caretaker,” or “my loving parent” more often than “father.” All of the women bless the communion bread and wine together. “There is a wide variety of opinions about what happens at the consecration,” said Dierks. “Some women say it is symbolic. Some say it is more.”

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Catholic teaching on this question is specific: “Only a duly ordained priest can consecrate bread and wine into the body and blood of Christ,” said Sister Mary Ann Walsh, a spokeswoman for the National Conference of Catholic Bishops in Washington, D.C.

“I see myself as defecting in place,” said Dierks, 56, a wife and mother of four. “The idea is to move toward a different church environment. There are women who want to be ordained, but in a reformed environment.”