People Before Profit TD Brid Smith claims the outsourcing of the CervicalCheck screening programme is at the heart of its latest scandal.
It was revealed last week that some 800 women did not receive the results of their tests in recent months.
One of the labs - Quest Diagnostics - based in the US state of Virginia had delayed issuing cervical screening results to some women and their GPs, due to IT problems.
The Health Service Executive (HSE) said the issue appeared to "primarily affect approximately 800 women" who were having HPV tests rechecked - dating from late 2018 until June 2019.
However, the Department of Health was only told last week about the IT glitch.
The HSE said it had known since February about the issue.
It also said it was aware of a "very small number of people" affected outside of this recheck group, and was following up on those cases.
The HSE is launching a rapid review process into the incident.
Deputy Smith is calling on Health Minister Simon Harris to commit to "repatriation" of the service.
She says: "It is outrageous that women's health is constantly being compromised by disclosure failures and delays".
She claims the latest delay for hundreds of women under the CervicalCheck scheme is further evidence that "outsourcing of the screening programme is at the heart of the problem."
"I will be tabling questions to the minister on his faith in the system of outsourcing and if he can guarantee women that they are receiving the best possible attention in this cancer screening programme.
"These delays in delivering results come on top of the massive backlog in the programme and that on top of the tragedies of many women needlessly suffering because the screening programme carried out 'on the cheap' in US labs failed them."
"It has to end and the Minister must indicate that he has faith in the system and if not he needs to make a commitment to change it and bring the service back into public labs in public control in the Irish health service."