The Health Service Executive has said it will be asking all of its hospitals to confirm that they do not have similar problems to Tallaght Hospital with delays in reviewing X-rays.
Dr Barry White, HSE National Director of Quality and Clinical Care, said that until that audit was completed, the Executive could not provide reassurance.
Dr White was speaking after a meeting with Tallaght Hospital management and doctors on the controversy.
He said the review of the remaining 23,000 X-rays at Tallaght can not be completed any faster than the May timescale already indicated.
The HSE is to carry out an investigation into the circumstances that led to the accumulation of X-rays not read by radiologists at Tallaght.
The investigation will be chaired by a person independent of the hospital and the HSE and details will be announced in the coming days.
The HSE said Professor Kevin Conlon, CEO designate of Tallaght Hospital, supports its investigation.
It also said it is fully supportive of Professor Conlon and the management team at Tallaght Hospital in dealing with the outstanding X-rays.
Call for Minister to resign
Earlier, Fine Gael's Health Spokesman Dr James Reilly said Minister for Health Mary Harney should resign over the problem of unread X-rays at Tallaght Hospital.
It was revealed yesterday that a patient died and another is being treated for cancer after almost 58,000 X-rays of adult patients, taken between 2005 and the end of last year, were never reviewed by a consultant radiologist.
Speaking on RTÉ's Morning Ireland, Mary Harney said she first heard there were problems in December, but that it was only yesterday when she first appreciated the scale of the problem.
Ms Harney last night said the priority is that the remainder of the backlog of X-rays be cleared, so that concerned patients could be reassured as soon as possible.
The Irish Hospital Consultants' Association has said that over 40 letters were written by consultant radiologists at Tallaght to management over a four-year period expressing concerns regarding the volume of work they were expected to do and were able to do.
IHCA Deputy General Secretary Donal Duffy said he was not aware of any replies.
Initial backlog thought to be 700 X-rays
In a statement today, Tallaght Hospital outlined the sequence of events leading to the revelations about the failures related to the checking of X-rays.
The hospital says that initially the number of X-rays involved was thought to be 700.
It was not until 14 December that a report ordered by Prof Conlon showed the true figure of unreported X-rays to be 57,921, the hospital said.
It added: 'The backlog in radiology was raised at the Board of the Hospital in May 2009, but the full extent of the problem was not clear until the new Chief Executive designate took up his appointment in December 2009.'
The Chairman of the Hospital Lyndon MacCann commented on revelations today that a Tallaght-based GP had written to him expressing concerns about the problem in April 2009.
Mr MacCann said that he only learned this afternoon that Dr Tom O'Dowd had done so.
Despite the letter having being stamped as 'received' by the Chief Executive's office on 27 April 2009, Mr MacCann said he had not known of this letter until today.
There are now two helpline numbers for people concerned about X-rays at Tallaght: 1800-283059, and 1800-283293.
They will now be in service from 8am to 8pm from tomorrow.