The Irish Independent reports that O'Brien put a halt to a report into allegations of abuse that was commissioned by The Bishops' Conference of Scotland in 2011. O'Brien was president of the conference at the time.
The Irish-born Scottish cardinal resigned in February after being accused by four priests of sexual exploitation.
In a letter to The Tablet, a Catholic newspaper, Mario Conti, the retired archbishop of Glasgow, revealed O'Brien's opposition to the conference's inquiry into abuse allegations.
"It was the intention of all but one member of the Bishops' Conference to commission an independent examination of the historical cases we had on file in all of our respective dioceses and publish the results, but this was delayed by the objection of the then president of the conference; without full participation of all the dioceses the exercise would have been faulty," wrote Conti.
A Church spokesman said: "This refers to a decision taken in 2011 by the Bishops' Conference of Scotland to commission an independent academic analysis of statistics relating to abuse and allegations of abuse over a 60-year period from 1952 to 2012.
"This project, with the cooperation of each of the eight dioceses in Scotland, started and ran until 2012, at which time, the then president of the conference, Cardinal Keith O'Brien, withdrew from the project. Without the participation of all the dioceses a 'national audit' was not possible so the analysis was stopped."
This June, the Bishops' Conference of Scotland agreed to publish the audits relating to the eight dioceses since 2006 this autumn.
The reports, "will detail any complaints made about clergy, church workers, volunteers or anyone else and how these complaints were dealt with," said the Church.
The spokesman added: "Prior to 2006 there was no National Audit and so at present, renewed consideration is being given as to how the statistics which exist for the earlier years can be drawn together and published.
"The Church remains willing to engage in any process which allows lessons to be learned and survivors to be supported."