The Minister for Justice is considering the establishment of a consultative committee on sexual violence. Mr McDowell told Ms Breeda Moynihan-Cronin (Lab, Kerry South) that he was "well disposed" towards that proposal, recommended in the Sexual Assault and Violence in Ireland (SAVI) report, published last year.
Ms Moynihan-Cronin said the findings of the report were "frightening" and that few women reported assaults because they were "terrified their case will become public".
There was also a lack of consistency in how judges approached and treated women who were raped or violently attacked.
The Fine Gael justice spokesman, Mr John Deasy, said 42 per cent of women experienced some form of sexual abuse and 28 per cent of men experienced sexual abuse, which equated to more than one million people.
But Mr McDowell said that by far the greatest category of reasons for non-reporting was that the victims thought the case was too trivial.
The Minister for Justice has to decide whether to do a "sticking plaster" refurbishment of Mountjoy Prison or to demolish and replace the existing buildings.
Mr McDowell said that the possibility of acquiring suitable lands in the Dublin area and surrounding counties "will have a major bearing on the decision".