The Opposition has moved to place the Taoiseach, Mr Ahern, at the centre of the controversy surrounding the departure of Ms Justice Laffoy from the inquiry into child abuse at residential institutions.
Fine Gael, Labour and the Greens yesterday called on Mr Ahern to make a statement on the affair.
The Fine Gael leader, Mr Kenny, said Mr Ahern should take personal responsibility for the work of the Laffoy Commission.
"It is clear that Minister Dempsey's ham-fisted review of the work of the commission was being carried out without adequate consultation with the chairwoman," he said.
"In the absence of more information, we can only speculate on the extent to which this contributed to her resignation."
Mr Kenny said the process had involved an inherent conflict, where Mr Dempsey's Department was sponsoring the work of the commission while also being subject to its investigation.
He added: "Responsibility for interfacing with the commission should be removed from the Minister and Department of Education. The Taoiseach should take personal responsibility for this and move responsibility for the work of the commission to his own Department."
Fine Gael's education spokeswoman, Ms Olwyn Enright, said the Government's refusal to publish Ms Justice Laffoy's resignation letter was a "desperate attempt to buy time" that would only add to the anxiety and hurt of abuse victims.
The Labour education spokeswoman, Ms Jan O'Sullivan, also criticised the failure to publish the letter, saying that it was an "unbelievable example of contempt and arrogance".
It was unacceptable for Mr Dempsey to suggest after yesterday's Cabinet meeting that the Government would not discuss the resignation for another week, she said. "Why has the Cabinet not discussed the urgent situation today? Do the victims of abuse not deserve that?"
Claiming that Mr Dempsey's response to the resignation was cack-handed, she said the failure to publish the letter would only add to confusion and uncertainty.
"The public is entitled to answers from the Taoiseach, as head of Government, about this deepening crisis," Ms O'Sullivan said.
"The Minister has not addressed the suspension by the Laffoy Commission of its investigation committee, which is the kernel of the problem. Nor has he outlined whether and when Justice Laffoy will be replaced. Nor has he indicated when the review of the operations of the commission will begin or be completed."
The education spokesman for the Greens, Mr Paul Gogarty, said Mr Ahern should recall the Dáil to debate the future direction of the commission. He said Mr Dempsey's decision to initiate a second review into the commission had thrown the process into disarray.
The judge's resignation had compounded the situation.
"It has been known for some time that the Laffoy Commission was not able to work effectively for a number of reasons," he said.
"For the sake of the victims we need to look at new terms of reference that get to the bottom of the events that took place and which do not facilitate the same level of legal challenge."
Mr Gogarty said abuse victims needed to have their voices heard.
Any new terms of reference should allow the commission to conduct its work "without being constantly subjected to legal challenge by church bodies and receiving half-hearted responses from the Department of Education".
