Two Roman Catholic archbishops in Australia have apologised for the "evil of sexual abuse" carried out by priests in their clergy, but insisted the Church never tried to silence victims.

In a written apology released late on Thursday, Sydney Archbishop George Pell and Archbishop of Melbourne Denis Hart said they wanted to work "towards healing".

We apologise, sincerely and unreservedly

Archbishops' statement

The apology comes days after Archbishop Pell angrily denied trying to cover up sex abuse cases in the 1990s.

He has admitted offering victims of abuse thousands of dollars in compensation but insisted the money was not "hush money" intended to silence them.

Archbishop Pell denies any wrongdoing

Archbishop Pell has refused calls from child abuse support groups that he resign over allegations against him, which were aired on Australian television on Sunday.

The two archbishops said the "integrity of the overwhelming majority of priests" was beyond question and urged victims of abuse to go to the Church for assistance.

"On behalf of the Catholic Church in Melbourne and Sydney, and personally, we apologise, sincerely and unreservedly, to all victims of abuse, and to the Australian community, for the wrongs and hurt suffered."

But one victim support group, Broken Rites, was critical of the statement and told the Sydney Morning Herald that the archbishops should be encouraging victims to go to the police, rather than the Church.