The Sisters of Mercy, which ran institutions in Galway and Dun Laoghaire, said it accepts the "limitations of the care" it provided.
"Their institutional setting was far removed from the response considered appropriate to such needs today. We wish that we could have done more and that it could have been different," the order said.
"It is regrettable that the Magdalene homes had to exist at all. Our sisters worked in the laundries with the women and, while times and conditions were harsh and difficult, some very supportive, lifelong friendships emerged and were sustained for several decades."
The Sisters of Our Lady of Charity of Refuge, which ran laundries at Drumcondra and Sean MacDermott Street in Dublin, said their intention for 160 years was to offer refuge.
"The laundries which were attached to refuges were hard and demanding places to work. Many women used our refuges as a place of last resort. There are also many who found themselves in a refuge through no choice of their own," the order said.
"Regardless of why a woman was in a refuge or how she came to be there, we endeavoured to provide care. It is with deep regret that we acknowledge that there are women who did not experience our refuge as a place of protection and care. Further, it is with sorrow and sadness that we recognise that for many of those who spoke to the inquiry that their time in a refuge is associated with anxiety, distress, loneliness, isolation, pain and confusion and much more."
The Sisters of Our Lady of Charity of Refuge said the challenge now was to move beyond denial, distortion and deletion to face the reality of how women came to be in a refuge, how they were treated and how they were treated on the outside.
The Good Shepherd Sisters, which ran workhouses in Limerick, Cork, Waterford and New Ross, said: "We were part of the system and the culture of the time. We acted in good faith providing a refuge and we sincerely regret that women could have experienced hurt and hardship during their time with us," the order said.
"It saddens us deeply to hear that time spent with us, often as part of a wider difficult experience, has had such a traumatic impact on the lives of these women."
The umbrella group for religious orders in Ireland, Conference of Religious of Ireland (Cori), said it hoped the report would bring reconciliation and healing.
"The Magdalene Homes issue was and is not just about religious, but also involved many other strands of Irish society," Cori said. "It represents a sad, dark and complex story, especially for the women involved, many of whom were rejected, isolated and hurt by a system, which failed to respond with empathy to their various needs."
Cori said a system of workhouse designed for the destitute and widely used across Europe was provided in good faith but "basic and inadequate when viewed in the 2013 context".