The national screening programme CervicalCheck has taken issue with claims that women may have been wronged by the system in the past, "whereas in fact they have been unfortunate in not being one of those to have cancer detected early".
It also said that Ireland was 'an outlier' internationally with its approach to compensation for cancers found between screenings.
CervicalCheck said that the current adversarial system is not in the best interests for patients, their families and their doctors.
"If the annual compensation costs for interval cancers exceed the total annual cost of running the screening programmes, screening will no longer be viable and it would be more ethical to reallocate funds to the acute symptomatic service," it says.
The remarks are made by the CervicalCheck Clinical Director, Dr Nóirín Russell in a letter dated 6 November, to TD Peadar Tóibín, who is Aontú party leader, regarding comments he made in the Dáil on 21 October.
"I worry that comments such as those you have made makes women feel they have been wronged by the system," the letter states.
In the letter, CervicalCheck says it is a huge psychological blow to receive a diagnosis of cancer and for a person to think they might have been wronged makes it even worse.
"This is best that any cancer screening programme in the world will ever be and therefore perpetuating the idea that these are mistakes is harmful to women and their confidence in the programme," CervicalCheck said.
According to Dr Russell, there is a 30-55% chance that abnormalities will be seen when looking back on screening tests and it is "misleading" and not factually correct to say these were mistakes or missed readings.
Mr Tóibín has said in response to the letter that he is alarmed that one arm of the State in CervicalCheck is saying something which is in complete contradiction to the Government and the courts in relation to the CervicalCheck crisis.