Minister Harris and the HSE director general, Tony O'Brien, have agreed that an global peer review of CervicalCheck needs to take place to ensure ongoing confidence in it.
"Am arranging for this facility to be available & the State will meet the cost of the repeat test. Arrangements on how this will operate will be outlined next week".
Ms Phelan was awarded €2.5 million in a settlement against the U.S. lab during the week, over a false negative smear test in 2011.
She was diagnosed with cervical cancer around the same time, but she only found out about that review a year ago.
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She told the HSE of her intention to resign saying she was sorry that recent events caused distress and worry to women.
"As soon as I heard the voice I knew who it was and he said "hi Vicky, it is Simon Harris here", Ms Phelan explained.
"Despite these achievements, every diagnosis of cervical cancer is one too many and we acknowledge the impact of this disease on women and their families".
Dr Flannelly said she had chose to step aside to allow the service continue its important work. "Doing so at a late stage, in the knowledge that you could have been diagnosed earlier is a harrowing experience, and it is saddening to see cancer patients on the steps of the High Court", it said.
"Figures from National Cancer Registry Ireland show that the cervical cancer rate in Ireland has reduced significantly as a direct result of the CervicalCheck programme". The Society has full confidence in the service, which we expect will progress from smear to HPV testing as a first-line test in the near future.
"Despite this, cervical screening represents one of the most effective ways to prevent cervical cancer".
The issue was brought to light when terminally ill Vicky Phelan, who had a missed abnormality in a 2011 smear test, won a High Court case last week. "No woman should have to wait this long for information relevant to their care", it said.