Dioceses and religious orders received 691 new allegations last year, compared with 714 in 2006.
The overwhelming majority of claims date back decades.
Settlements with victims increased by 90 percent over the same period, to more than $526 million — the largest amount for one year.
The findings, released Friday, are part of an annual review the American bishops commissioned in 2002 as the abuse crisis consumed the church.
A companion audit of bishops' child safety policies found that nearly every diocese was following the plan.
Still, the bishops' child protection officer cautioned against "issue fatigue."
Teresa Kettelkamp, executive director of the Office of Child and Youth Protection, said the sense of urgency surrounding the issue is easing as dioceses finish enacting the reforms and cope with the many other demands on their resources.
Auditors found that some lay-clergy review boards — created in every diocese to help bishops respond to abuse — hadn't met in more than a year because no new allegations had been made.
Two archdioceses — Denver and Anchorage — hadn't reported abuse claims to civil authorities until after the lapse was discovered in the audit.
"I think this is too important an issue to tire of it," Kettelkamp said. "Just because the number of victims has decreased, don't feel that there aren't more victims out there needing encouragement to come forward."
The abuse crisis erupted in 2002, with the case of one predator priest in the Archdiocese of Boston, then spread to dioceses nationwide and beyond.
The bishops responded by enacting the Charter for the Protection of Children and Young People, which requires dioceses to conduct background checks on workers, provide safety training to children and reach out to victims.
Nearly 14,000 molestation claims have been filed against Catholic clergy since 1950, according to tallies released by the bishops' conference. Abuse-related costs have reached at least $2.3 billion in the same period.
Last year, total abuse-related costs, including settlements, legal fees, therapy for victims and support for offenders, surpassed $615 million for dioceses and religious orders.
Several dioceses reached massive agreements with victims in the past 12 months.
The Archdiocese of Los Angeles had the biggest by far, pledging $660 million to about 500 people. But many of those settlements have yet to be fully paid. Insurance covers some of the cost.
Of the 691 new abuse claims, five cases involved alleged victims who were under age 18 last year. Some of the accused clergy in these cases were overseas priests working in the United States.
The National Review Board, the lay panel the bishops established to monitor their policies, said dioceses should improve background checks on priests from other countries and review standards of conduct with them.
American dioceses are relying increasingly on overseas priests as the number of U.S. clergy sharply decline.
Most of the new allegations were made by adults who said they had been abused about three decades ago.
A large majority of the 491 clergy accused last year were dead or missing, or had either been barred from public church work or defrocked because of other molestation cases.
About 40 percent of the clergy was newly accused.
The survey of nearly all 195 U.S. dioceses and non-geographic districts called eparchies was conducted by the Center for Applied Research in the Apostolate at Georgetown University.
The accompanying audit was conducted by The Gavin Group, Inc., a consulting firm led by a former FBI official, which completed onsite reviews at 190 dioceses and eparchies nationwide.
Four eparchies and the Diocese of Lincoln, Neb., did not participate.
The biggest compliance problem the auditors discovered was training children to protect themselves from abuse. Eleven dioceses had not fully completed the training.
Kettelkamp said it has been especially difficult to train children in after-school religious education classes, who often only attend for a short period.
The Archdiocese of Boston was among those that failed to provide training in those courses.
Advocates for victims have criticized the annual reports because the auditors and researchers must rely on information provided by the dioceses and religious orders.
"It's tempting but irresponsible to assume progress has been made at this very premature stage," said David Clohessy of the Survivors Network of those Abused by Priests.
"There always has been and always will be a lag time in reporting abuse."
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