The government has begun digesting yesterday's report which highlighted state collusion in the laundry system.
Representatives of the survivors of Magdalene laundries and their families say Enda Kenny's statement in the Dáil yesterday does not go far enough.
The Justice for Magdalene group says it wants an apology from the religious orders, but a full apology from the State would be the most meaningful.
Yesterday, the Taoiseach said he was sorry for those people who lived in the kind of environment described in the report.
But srvivors have expressed their dismay at the Taoiseach's apology and are calling for a suitable compensation package.
SIPTU's Equality and Campaigns Organiser Ethel Buckley says it should provide for pensions and lost wages as well as health and housing services.