Turning the scoping inquiry into Cervical Check into a full Commission of Investigation needs to be considered, according to Taoiseach Leo Varadkar.
The Fianna Fáil leader Micheál Martin has called for a full Commission of Investigation.
It comes after the head of the inquiry revealed on Tuesday he has had trouble getting documents from State agencies.
Dr Gabriel Scally said his report into the non-disclosure of smear test audits to 209 women will now be delayed until the end of the summer.
In his progress report, Dr Scally observed: "It is disappointing and unclear why documents that would originally have been prepared in electronic format (including some very recent documents) are not available to the Inquiry in that format, rather than as a scanned version of the printed copy."
Speaking in the Dáil earlier, Mr Martin said it is time to give the current investigation more teeth.
He said: "We're now looking potentially at a Commission of Investigation starting up in November - if we're lucky - at the current rate of progress.
"I think putting Dr Scally and his team on a statutory basis in the format of a Commission of Investigation may be the most effective way to give teeth... to ensure there's no more messing, no more withholding of documentation and the kind of stuff that's gone on so far."
The head of the investigation said his report will be delayed until the end of the summer because he's still waiting on documents from state agencies.
Mr Varadkar has said making it a full Commission should be considered, but the scoping inquiry has been shown to have advantages.
"We already have a progress report, we already have an interim report, we already have findings and recommendations related to one of the terms of reference.
"And those recommendations are already in the process of being implemented".
The Government has said Dr Scally will continue with the scoping inquiry and provide further reports as his work progresses.
In a tweet earlier, Health Minister Simon Harris insisted: "Let me be crystal clear whatever information Dr Scally requires, he must be provided with. I made that absolutely clear when I met him yesterday."
Let me be crystal clear whatever information Dr Scally requires, he must be provided with. I made that absolutely clear when I met him yesterday. I am grateful to him for his excellent work, his engagement with the women impacted & 6 key recommendations which I accepted in full
— Simon Harris TD (@SimonHarrisTD) June 12, 2018
Reporting by Sean Defoe, Stephen McNeice and Jack Quann