Mr Harris has also said the State should not be defending court cases against women such as Vicky Phelan, who has terminal cancer.
The Government is expected to confirm a statutory inquiry later today.
It's led to widespread concern about the screening programme, and Taoiseach Leo Varadkar, a doctor himself, says serious questions need to be answered.
More than 2,000 women have called the CervicalCheck helpline over the weekend.
It also showed that half of the 206 women affected by the inaccuracies were not told that they may have a delayed diagnosis.
The current controversy centres around cases where CervicalCheck, the national cervical cancer screening programme, did not inform women who developed cancer after audits found past smear tests incorrectly gave them the all-clear.
"Five year undetected pre-cancerous cells, you're looking at 30-40% of the women not surviving", said Deputy O'Connell.
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The line will stay open until 6 o'clock this evening and the HSE says call-backs are underway.
The figures were released following the controversy surrounding Vicky Phelan (43), a mother of two from Limerick, who was given incorrect cancer results and is now terminally ill.
Overall, 206 women with cervical cancer who had smear tests should have received earlier intervention than they did, the HSE noted.
Meanwhile, GPs are urging women to continue with their Cervical Checks.
"We're carrying out roughly 250,000 smears per annum, we're after reducing the incidents of cervical cancer by 7%", said Dr Jordan.
Those wishing to contact the helpline can do so on Freephone 1800 45 45 55.
She said she had made a decision to step down "to allow the programme to continue its important work" and she apologised to women who have been distressed by recent events.