"The single quickest and most effective step would be for the next pope to clearly discipline, demote, denounce and even defrock cardinals and bishops who are concealing child sex crimes. We think that's the missing piece," he said.
The new pope should order each bishop around the world to hand over "every piece of paper he has on proven, admitted or credibly accused child-molesting clerics to law enforcement," Clohessy said.
Barbara Dorris, victims' outreach director for SNAP, said: "The short answer is we've tried silence, silence didn't work, so we have to speak out. We have to do everything we can to get this information out there."
The Catholic Church has been rocked by a series of child sex abuse scandals in recent years -- and the new pope will be under pressure to deal more effectively with a crisis that has shaken public confidence in the church.
SNAP says it's vital to look at how the world's bishops have handled claims of abuse by priests because the crisis is far from over.
"This scandal, we believe, has yet to surface in most nations. It's shameless spin and deliberate deception to claim otherwise. It's tempting to reassure the public and the parishioners by making this claim. But it's also irresponsible," a statement on SNAP's website said.
"Clergy sex crimes and coverups remain deeply hidden in the vast majority of nations (where most Catholics live), and has really only become widely known -- and barely addressed -- in the U.S. about a decade ago and in a few European countries even more recently."
Media leaks concern
A news conference scheduled by American cardinals for Wednesday, following media briefings on Monday and Tuesday, was canceled at short notice.
Asked if the Vatican had told the American cardinals to stop their daily media briefings, Vatican spokesman Rosica suggested that the details of what was discussed in the general congregations were not meant to be publicized.
"It's not up to Father Lombardi or myself to tell them what to do," he said. "It could be that among themselves they realized that there are different ways and different methods of getting things out."
Sister Mary Ann Walsh, director of media relations for the U.S. Conference of Catholic Bishops, said via e-mail that the U.S. cardinals were committed to transparency and had wanted to share "a process-related overview of their work" with the public "in order to inform while ensuring the confidentiality" of the general congregations.
"Due to concerns over accounts being reported in the Italian press, which breached confidentiality, the College of Cardinals has agreed not to give interviews," she said.
In total, 153 cardinals gathered Wednesday at the Vatican for a third day of meetings, known as general congregations, before they set the timetable for the election.
The cardinals spoke about new evangelization, restructuring of the church hierarchy, or curia, and the need for good governance of the church, Lombardi said.
A five-minute limit has been imposed on cardinals speaking at the meetings, although the microphone is not being switched off if they run over the time allowed.
The cardinals have decided to meet twice Thursday, in the morning and afternoon, in order to "intensify the rhythm of work," Lombardi said.
Video shown at a Vatican news conference showed workers preparing the Sistine Chapel for the secretive conclave.
An elevated floor is being put in place to protect the elaborate mosaic tiling, said Lombardi, where seats will be placed for the cardinals.
The Sistine Chapel and its ornate ceiling by Michelangelo are normally a must-see for tourists in Rome, but it was closed to the public beginning Tuesday afternoon to allow for preparations to take place.