Cardinal Christoph Schoenborn said efforts by the then Cardinal Joseph Ratzinger to investigate a 1995 case were blocked by then Pope John Paul II.
Cardinal Schoenborn said the Vatican had argued an investigation would generate bad publicity.
The cardinal's comments follow a week when the Vatican's record on child abuse has been intensively scrutinised.
Cardinal Schoenborn told Austrian television that the current Pope tried to establish a Church investigation into abuse allegations against a previous Archbishop of Vienna, Cardinal Hans Hermann Groer.
The Austrian Church was rocked by allegations in 1995 that Cardinal Groer had molested youths at a monastery in the 1970s.
But it was not until 1998 that, on Vatican orders, Cardinal Groer relinquished all religious duties and sought exile in Germany. He died in Austria in 2003.
At the time of his resignation, Cardinal Groer, in a statement released by the Church in Vienna, asked for forgiveness but made no admission of guilt.
At the time, the Vatican drew sharp criticism from many Austrians for taking three years to act against Cardinal Groer.
Cardinal Schoenborn, who replaced Cardinal Groer as Archbishop of Vienna in 1995, said Joseph Ratzinger was blocked in his efforts to confirm if there was a case to answer.that the allegations were exaggerated and that an investigation would open the Church up to negative publicity.
"I can still very clearly remember the moment when Cardinal Ratzinger sadly told me that the other camp had asserted itself," Cardinal Schoenborn told ORF television.
"To accuse him of being someone who covers things up - having known the Pope for many years - I can say that is certainly not true," he added.
This is not the first time that Christoph Schoenborn has intervened in the scandal currently confronting the Church.
Earlier this month, he said clergy celibacy should be examined in trying to uncover the causes of abuse by priests.
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