The TD said that he plans to work with the Government to avoid any more mishaps.
Simon Harris has said he does not know how many women may have died from the recent cervical smear controversy.
Speaking on RTÉ's The Week in Politics, the Health Minister said that he hopes to know by Monday if all of the 206 women affected, or their families, have been contacted.
Harris also said that he hoped the HSE or the State would not defend any other cases that may be similar to the Vicky Phelan case, adding that he plans to work with the Government to avoid it.
During the week, the Fine Gael TD announced that he is currently organising for
repeat smear tests to be arranged free of charge following the recent news that several cases of cervical cancer have gone misdiagnosed.
Harris took to Twitter on Saturday to share the news of the repeat tests on offer, which, according to him, will be paid for by the State.
Saturday night saw the HSE confirmed that the clinical director of Cervical Check, Dr Gráinne Flannelly, had stepped down from her post effective immediately, in wake of the recent cervical cancer scandal.
It follows days of uncertainty, over what an unpublished 2014 HSE audit of cervical checks discovered.
Vicky Phelan, the terminally ill woman who brought this issue to light,
appeared on the Ray D'Arcy Show on Saturday night to share her story of misdiagnosis.
She revealed that Simon Harris had called her personally to apologise for the health service letting her down.
