Enda Kenny said he expects Justice Minister Alan Shatter to bring the report to Cabinet this month when the Government will consider recommendations for a redress process.
"Once the process is decided upon, there will be no delay on the Government's behalf in following through on this," Mr Kenny said.
"I do hope it will be possible, together with the women involved, to deal with that process and deal with it in their interests."
The Taoiseach rejected accusations he was "playing games" with the lives of the victims – many of whom are elderly and infirm – by having taken so long to consider the report by retired High Court judge John Quirke.
Mr Shatter received the report a month ago. It is understood to include recommendations for a reconciliation forum between Magdalene survivors and the four religious orders that ran the Catholic institutions.
Other mediation measures are reportedly proposed to help establish what financial compensation will be made to the survivors.
Mr Kenny said he wanted to ensure the Government has time to consider the compensation scheme.
"The report will come to Government in the next two weeks. The Government will consider the recommendations of the report and the views of the minister for justice in it, and the Government will make its decision," he said.
He said the report would be published "immediately" after it is brought to Cabinet.
The Taoiseach made a tearful apology to the Magdalene survivors in February after an inquiry from former senator Martin McAleese revealed the state had a hand in 24% of admissions to the laundries.
His probe found that 10,000 women were incarcerated in the workhouses, run by nuns from four religious orders, for a myriad of reasons – from petty crime to poverty, disability or pregnancy outside marriage.
The last laundry closed in 1996, at Sean MacDermott Street in Dublin's north inner city.
"Having waited some 60 or 70 years, I think it's only right and proper that this deserves real consideration by the minister for justice," Mr Kenny said.