Mr Kenny again refused today to make a full apology to the remaining survivors.
He turned on Sinn Fein in the Dail for demanding an apology, when it has failed to say sorry for IRA atrocities.
The Taoiseach said the report by former Senator Martin McAleese into the Magdalene Laundries "makes for harrowing reading in many respects".
Survivors of the laundries have fiercely criticised the Government's response after a report yesterday revealed a quarter of the 10,000 plus women detained in horrific regimes in the institutions were sent by state authorities.
Mr Kenny was accused of a "cop-out" and "mealy-mouthed apology" after he said he was sorry for the stigma attached to the women, but stopped short of issuing a full and frank apology on behalf of the country.
"This is not a matter for idle comment or flippant politics. It is of intense seriousness for those involved and for those who have responsibility now," the Taoiseach told the Dail today.
"I want to repeat again my sense of deep sorrow for all those women who went through that regime."
"On behalf of this State, I am absolutely sorry for all that happened in the Magdalene laundries," he said.
Fianna Fáil leader Micheal Martin, Sinn Fein deputy leader Mary-Lou McDonald and Independent TD Mattie McGrath all called for Mr Kenny to make a full apology.
But the Taoiseach said he did not want to see any "adversarial diplomacy on an issue that is so sensitive".
He appealed for time and space to study the report before deciding how to respond to the needs and requirements of the survivors of the laundries.