They said the findings of the National Board for Safeguarding Children in the Catholic Church report revealed bishops had made efforts to modernise and improve their handling of abuse cases.
However, they said shortcomings remained and these needed to be addressed by statutory bodies outside the influence of the Church.
Executive director of One in Four, Maeve Lewis, said in the case of each of the six dioceses audited there had been obvious improvements in the handling of allegations.
And she particularly welcomed the recommendation that dioceses should employ an independent and experienced child protection officer rather than having victims make statements to people within the diocesan organisation.
"Many victims believe they are meeting a support person when in fact the [child protection] delegate has an investigative function.
"We are concerned at instances where the delegate records and relayed the details to the alleged perpetrator, potentially undermining a future criminal investigation," she said.
Ms Lewis also called on all other dioceses in the country to follow the lead of the Raphoe, Derry, Dromore, Tuam, Kilmore, and Ardagh and Clonmacnoise.
Executive director of Amnesty International Ireland, Colm O’Gorman, said while the audits were welcome, they remained documents which were published with the permission of the bishops and they were not the same as statutory inquiries.
And Mr O’Gorman said the audit raised issues which would have to be dealt with it.
"The examination of the Diocese of Raphoe, for example, is particularly worrying. It highlights concerns over the approach adopted to child protection complaints by three bishops, including Bishop Dr Philip Boyce, and concerns about the system for protecting children as late as 2009.
"It is also clear that individuals were appointed to child protection roles they were not comfortable with, and that while particular care was taken to support priests who were the subject of complaints, the individuals who made the complaints received little attention," he said.
The Dublin Rape Crisis Centre said despite the welcomed progress, those who suffered at the hands of the priests may not feel the audits of current practices did enough to expose the wrongdoings.
"The clients availing of the services of the Dublin Rape Crisis Centre whose allegations were not handled appropriately in the past may not find much comfort in these reports.
"We would hope that the apologies that are repeated in the reports will go some way to helping these survivors on their road to recovery," its chief executive Ellen O’Malley Dunlop said.
Help lines
* Garda Confidential Line: 1800 666 111
* Dublin Rape Crisis Centre: 1800 77 88 88
* Faoiseamh, a help line funded by the Council for the Religious in Ireland and various Catholic diocese: 1800 331234
* One in Four: 01 6624070