Noirín O'Sullivan has come under pressure following the latest controversies involving the force
The Garda Commissioner is to hold a press conference this afternoon as she faces mounting calls to resign or be dismissed.
The Tánaiste and Justice Minister Frances Fitzgerald did not ask the Commissioner to resign when they met earlier.
Opposition parties are unhappy with Noirín O'Sullivan's explanations for revelations that thousands of people were wrongly convicted in court of motoring offences, while breath tests were exaggerated by around one million.
Sinn Féin has published a motion of no confidence in her, while Fianna Fáil and other parties demand a full explanation from the Commissioner.
At the weekend, the Commissioner said the revelations over penalty points and Garda breath test errors were "totally unacceptable" .
In a statement, she said: "I am determined that where we identify problems in the organisation, we admit these issues publicly, take whatever corrective action is necessary and ensure they do not recur.
"That is what I expect of the organisation and what is demanded of us by the community.”
Sinn Féin justice spokesperson Jonathan O'Brien, however, claims it is time for the Commissioner to go.
“It is clear public confidence in An Garda Siochana would be further eroded by Noirin O’Sullivan remaining as Garda Commissioner," he argued.
"Her position has become untenable. The Government should now use the power provided to it, under the 2005 Garda Siochana Act, to remove her from office."
Social Protection Minister Leo Varadkar says the Government has confidence in Noirín O'Sullivan and believes she is part of the solution and not the problem.
"I would really ask opposition parties not to try and exploit this, or play politics with this," he said.
"[I'd ask them] to desist from putting down a motion at least until such a time as the Cabinet has an opportunity to discuss it, and the Garda Commissioner has an opportunity to account further."
Minister Fitzgerald last week said she had outlined her "very serious concerns" to the Commissioner.
Speaking to Newstalk Breakfast, Fine Gael TD Alan Farrell said it is important to find out who is responsible.
"I think the Commissioner has taken this matter on, and identified a course for resolution," he argued.
"What we need to determine in the course of this investigation - and through the conversation that the Tánaiste is going to have with the Garda Commissioner this morning - is to verify that the problems that are there, and the questions that need to be asked [...] will be answered."
Over the weekend, Micheál Martin said that Fianna Fáil cannot express confidence in the Commissioner.
Last week, Garda officials revealed that 147,000 court summonses were issued between 2006 and 2016 for offences that did not require them.
Of those, 96% were included alongside other offences that could have landed them in court - but almost 6,000 were stand-alone and should have received a fixed charge notice instead.
Thousands of drivers are likely to have their penalties overturned as a result.
The force has also admitted that there is a huge discrepancy in their recorded breath test figures.
Official figures showed there were 1,995,369 roadside tests logged between 2011 and 2016 – however it has now emerged that almost one million of these never occurred.
Frances Fitzgerald has said she had made it clear to Commissioner O’Sullivan that “robust, tested and verified” new systems will have to be put in place to avoid any future mistakes.