Labour leader Ivana Bacik said there should be a broad inquiry that looks at every aspect of the scandal and at the existence of institutional cover-ups.
Tánaiste Leo Varadkar said the Government was considering a victim-led inquiry into schools run by the Spiritans, where more than 300 allegations have been made against 78 members.
But opposition parties are now calling for the Government to widen the scope of any inquiry after other congregations confirmed allegations were made against their members.
Glenstal Abbey boarding school in Co Limerick said it has records of four historical abuse allegations against two members of the Benedictine community.
“There have been no criminal or civil proceedings,” a spokesperson told the Irish Independent. “Financial settlements were made in some of these cases.
“In each settlement, and by mutual consent, we are bound by a confidentiality agreement.”
The Vincentian community said 45 allegations were made against nine priests, and 17 of these were from past students who attended Castleknock College, St Paul’s in Raheny, St Peter’s National School in Phibsborough, all Dublin, and St Patrick’s College in Armagh.
Twenty-nine of the allegations were made against one priest.
To date the Vincentian congregation has paid out €1,015,000 in compensation and €436,150 in legal fees.
The Vincentian community believes further allegations might be made.
Ms Bacik said any inquiry into abuse “must be survivor-led and must seek to review the extent of the abuse and, crucially, the existence of institutional cover-ups in individual schools and by particular orders”.
She also said: “It should also seek to examine the role of the State and in particular the failures of the State, what the State could and should have done to prevent abuse in schools where the teachers were paid by the State and the schools were receiving significant public funding.”
The Vincentian congregation said nine priests accused of abusing children had since died.
While the majority of allegations were of sexual abuse, two were allegations of bullying and physical abuse.
A spokesperson for the Vincentian community said all the allegations were made in the past 15 years and dated back to the 1950s.
However, “concerns” have also been raised about a number of other priests, but no formal allegations have yet been made.
“There is one allegation from a former pupil of one of our schools against a priest who is still alive,” the spokesperson said. “This allegation is currently under review by the statutory authorities and the priest in question is not in active ministry.”