Kenny stopped short of a full apology for the state's role in sending women to the laundries, The Irish Times reported.
"I want to see that those women who are still with us, anywhere between 800 and 1,000 at max, that we should see that the state provides for them with the very best of facilities and supports that they need in their lives," Kenny said in the Dail or parliament.
A report released Tuesday said the state was involved in some way in more than 26 percent of the referrals. The panel headed by Sen. Martin McAleese also said much of the laundries' income came from state contracts.
The Magdalene asylums, usually called laundries in Ireland, were founded in the 18th century, originally as a Protestant organization. In Ireland, the Catholic Church assumed control in the 19th century, and they were run by four orders of nuns.
The McAleese report covered the years between 1922, when Ireland became independent, and 1996, when the last laundry closed. The panel found there were about 10,000 residents during those years, most of them spending less than a year.
The popular image is that the laundries were for "fallen women," many of them prostitutes. But McAleese said referrals came from many institutions, including the courts, psychiatric institutions, families and priests. Some of the residents ended up in the laundries when they aged out of orphanages and children's homes.
McAleese described the laundries as "lonely and frightening places." But he said surviving residents do not report the kind of physical abuse that was routine at the time in Ireland's industrial schools.
"None of us can begin to imagine the confusion and fear experienced by these young girls, in many cases little more than children, on entering the laundries, not knowing why they were there, feeling abandoned, wondering whether they had done something wrong and not knowing when -- if ever -- they would get out and see their families again," McAleese wrote in the report.
Notable deaths of 2014 [PHOTOS]