The head of the Catholic Church in Germany apologized on Tuesday "for all the failure and pain" after a report found thousands of children were sexually abused by its clergy, a number an expert said was only the "tip of the iceberg".

Researchers of three German universities examined 38,156 personnel files spanning a 70-year period ending 2014, and found indications of sexual abuse by 1,670 clerics, with more than 3,700 possible victims.

German magazine Der Spiegel reported the findings earlier this month after the report was leaked. The scandal comes at a time when the Catholic Church is grappling with a number of new sexual abuse cases in countries including Chile, the United States and Argentina.

"For too long in the Church we have looked away, denied, covered up and didn't want it to be true," Cardinal Reinhard Marx, chairman of the German Bishops' Conference said at a news conference for the launch of the report in the central German city of Fulda on Tuesday.

"For all the failure, pain and suffering, I must apologies as the chairman of the Bishops' Conference as well as personally," Marx said.

"The study opened our eyes to the fact that this issue has not been overcome," he said.

Harald Dressing of the Central Institute of Mental Health said that number represented only the lower bound of estimates as many cases were likely never reported or not taken seriously enough to make note of them in the files.

"The resulting numbers are the tip of an iceberg whose actual size we cannot assess," Dressing said at the news conference.