Taoiseach Leo Varadkar has said he is "very dissatisfied" that the review of around 3,000 smear tests has not started.
However, Mr Varadkar said "preliminary work was being done" and the independent bodies carrying out the work had to be given the time to do it without Government interference.
"But certainly we had thought back in May that this was a job that could be done more quickly, but we're obviously going to do everything we can to make sure that work is done as quickly as possible."
The Department of Health confirmed today that an independent physical review of around 3,000 cervical smear slides has still to begin,
The review had been expected to be completed by the end of May.
Labour Party health spokeman Alan Kelly said Minister for Health Simon Harris should not have given a commitment that the review would be completed by May.
On RTÉ's Six One News, Deputy Kelly said there is no indication yet of when the review will begin and that confidence needs to be given to women about the cervical screening programme.
He said the review could have been conducted in time if the will was there but it emerged today that there are questions about the determination and in some cases the motives of the Health Service Executive to get the necessary work done.
The HSE and CervicalCheck were both before the Public Accounts Committee to provide an update on the screening controversy, which first emerged in late April.
The HSE told the committee that as of today the number of women affected has increased from 209 to 221.
It said the review of the 3,000 smear tests will take around four to six months and will not be available to the Scally Review given that timeframe.
Dr Gabriel Scally was appointed by the Government to conduct a preliminary inquiry into the cervical cancer controversy.
Deputy Kelly said that his direct message to Minister for Health Simon Harris is that unless he intervenes, Dr Scally's report will not be comprehensive.
Meanwhile, the Tanáiste told the Dáil that he understands that the Royal College of Obstetricians and Gynaecologists review is "about to take place".
However, Simon Coveney also said the Government could not "impose a timetable" on the organisation, which was independent and had its own procedures to follow.
He was responding to Fianna Fáil TD Dara Calleary who said the Taoiseach had previously committed to completing the review by the end of May.
Number of women affected rises to 221
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Earlier, Minister Harris said that the review of cervical smear test slides will begin "very, very shortly".
Speaking on his way into Government Buildings, he said the Royal College of Obstetricians and Gynaecologists in the UK have already begun work in relation to this, and there is "a huge body of work to be done".
He said the external review would help to build confidence in the cervical screening programme.
Mr Harris said: "I expect it will start reviewing slides very, very shortly, but I think it’s important that they get this right.
"This process is about externally validating our screening programme to make sure it’s the best."
When asked what was causing the delay, Mr Harris said it was "just a huge body of work and it was important to get it right."
"It is about learning from the mistakes of the past where audit wasn’t carried out appropriately in terms of learning from mistakes."
The department said the terms of reference and the scope of the review have been agreed and that work is under way.
The terms of reference have not yet been published.
"Required resources are currently being scoped, identified and put in place" by the HSE and the Royal College of Obstetricians and Gynaecologists, it said.
The department said that the "preparatory work ahead of actually looking at the slides, is under way and has been for a number of weeks".
It said that a large body of work is required before the slides can be looked at in a laboratory.
The review is to be carried out by the Royal College of Obstetricians and Gynecologists with expertise provided through the British Society for Colposcopy and Cervical Pathology.
It will deal with 1,482 cases notified to CervicalCheck and a further 1,630 cases registered with the National Cancer Registry.
Meanwhile, Sinn Féin's health spokesperson has questioned the Government's sense of urgency in getting to the bottom of the cervical smear controversy.
Speaking on RTÉ's Today with Sean O'Rourke, Louise O'Reilly said she did not think the Government was serious about taking action required, and that their sense of urgency seems to have disappeared.
Consultant in call for State-funded cervical cancer treatment trial
A consultant medical oncologist at St Vincent's University Hospital in Dublin has called for a trial of a new drug to treat cervical cancer to be established in Ireland.
Speaking on RTÉ's Morning Ireland, Dr David Fennelly who is treating Vicky Phelan with the drug, said a State-funded trial would be the quickest and most cost effective way to establish the trial.
Ms Phelan, who has terminal cancer, was awarded €2.5m earlier this year after she received an incorrect smear test result.
He said the key thing was that the drug offers an exciting potential for improvements for a wide variety of patients with malignant disease who have had very limited options in terms of treatment.
Dr Fennelly added that because doctors could predict a patient's response to the drug, doctors can select who will benefit most from it.
"We are in a situation in Ireland where we now have a group of women who unfortunately are going to be diagnosed with metastatic cervical cancer. Based on the experience we have in Vicky's case we are going to look to test them for [compatibility] and we are going to look to treat them with Pembrolizumab."
The drug is not currently licensed in Europe to treat cervical cancer.
Additional reporting Justin McCarthy