BERLIN — More than 3,600 children, most age 13 or younger, were sexually abused by Catholic clergy members over the past seven decades, a wide-ranging report has found.

The study, which was commissioned by the Roman Catholic Church bishops’ conference in Germany, found that at least 1,670 church workers had been involved in the abuse of 3,677 children. That is 4.4 percent of the clergy.

The study, conducted by researchers from three universities over more than four years, was an ambitious effort to understand the scale of the abuse — and how it could have been systematically covered up for so many decades.

“We are aware of the extent of the sexual abuse that is supported by the results of the study,” said Bishop Stephan Ackermann of Trier. “It is depressing and shameful.”