Mr Gilmore said bishops who were criticised for their failures in respect of children who were victims of child abuse should be removed from being patrons of schools, from serving on boards of hospitals or from the running of youth services or from any other services funded by the Irish taxpayer.
He said whether bishops remain in office as bishops is a matter for the church.
Mr Gilmore was speaking to journalists in Belfast after he had a series of meetings with political leaders at Stormont.
Mr Gilmore's comments come after Bishop of Killaloe Willie Walsh said that calls for the resignation of Bishop of Limerick Donal Murray are based on a misreading of the Murphy report into clerical child sex abuse.
Bishop Walsh refused to back growing demands for senior clergy criticised in the report to stand down and said damning findings were being misread.
Pressure has mounted on Bishop of Limerick Donal Murray to resign after an inquiry into the handling of child abuse cases in the Catholic Dublin Archdiocese branded his failure to investigate a paedophile priest inexcusable.
Speaking on RTÉ's Morning Ireland Bishop Walsh said: 'I do know that there has been gross misreading of the Dublin report in relation to Bishop Murray. There has been very serious misreading of that.'
Judge Yvonne Murphy found hundreds of child abuse allegations were covered up by senior clergy over a 30-year period because they were obsessed with secrecy and upholding the reputation of the church.
Bishop Walsh went on: 'I'm quite uncomfortable with this kind of public trial. I'd have to ask: is it about healing of survivors or is it about some sort of desire that we need to get a head on a plate?'
Amid calls for his resignation, Bishop Murray told parishioners in Limerick yesterday that he would be guided by the priests and people of his diocese.
Rank-and-file clergy, survivors of abuse and opposition politicians have said churchmen implicated in the report who still hold a position of power should resign.
Defence Minister and Limerick TD Willie O'Dea said he was sure that Bishop Murray, who he knows personally, was examining his position and would take the appropriate action.
Taoiseach Brian Cowen refused to be drawn into the controversy and said it was for institutions and their members to determine the appropriateness of any individual to hold ecclesiastical office.
Bishops have also refused to call for resignations.
Archbishop of Dublin Diarmuid Martin, who has been credited for opening secret church files to investigators, said he had no authority to ask anyone to resign over the scandal.
However, he revealed that a bishop could be removed if criminal proceedings are brought.
The Garda Commissioner has said that no serving garda was criticised in the report.
In his first public comment on the report, Fachtna Murphy said that there was no place in the force today for the level of deference that was shown to members of the Catholic Church in the past.
He said the investigation now being carried out by Assistant Commissioner John O'Mahoney would look at the handling of allegations of clerical sexual abuse, not just by gardaí, but all church and State authorities.
He said the Assistant Commissioner would act without fear or favour, and he rejected calls for an outside body to be brought in to investigate.
+++++++++++++++++++++++++++++++++++++++++++++
Disclaimer
No responsibility or liability shall attach itself to us or to the blogspot ‘Clerical Whispers’ for any or all of the articles placed here.
The placing of an article hereupon does not necessarily imply that we agree or accept the contents of the article as being necessarily factual in theology, dogma or otherwise.
SIC: RTÉ