Fianna Fáil says it is still not in a position to express confidence in the Garda Commissioner amid the continued controversy over Garda breath tests.
The party says it wants to hear more from Noirín O'Sullivan when she appears before the Oireachtas Committee on Thursday.
Yesterday, Commissioner O'Sullivan said an internal investigation will get to the bottom of how Garda breath test figures were exaggerated by almost a million.
She also insisted she will stay in her position to continue a programme of reform.
Minister Fitzgerald, meanwhile, has been updating her ministerial colleagues on the situation at today's Cabinet meeting.
Over the weekend, Fianna Fáil leader Michéal Martin said his party could not express confidence in Commissioner O'Sullivan following last week's revelations.
Today, the party's justice spokesperson Jim O'Callaghan said he has several questions for the Tánaiste and other ministers.
He said: "I want to hear from Frances Fitzgerald in respect of when she and the Government first became aware of the issues in respect of the breath tests.
"When did the Government become aware that the Garda figures were inaccurate or misleading, and what did the Government do in respect of that?"
Housing Minister Simon Coveney told reporters he believes the Garda Commissioner's position is still tenable.
"I think the core issue here is that we look at a process to ensure some of the failings in An Garda Síochana don't reoccur in the future," he said.
Opposition response
Opposition parties are still deciding on how they will respond to a motion of no confidence in the Commissioner being put forward in the Dáil by Sinn Féin.
Yesterday evening, Fianna Fáil called for an 'urgent' appearance of Minister Fitzgerald in the Dáil to answer questions about the Garda crisis.
Labour leader Brendan Howlin said the "silence of the Tánaiste over the last few days has been startling".
Speaking on Newstalk Breakfast this morning, he suggested a systemic change is needed in the force.
However, he would not be drawn on whether he will support the motion of no confidence in Noirín O'Sullivan.
He argued: "I think we need to look at the 2000 recommendations from the Garda Inspectorate, which would profoundly change the way we do policing in this country.
"We need to have someone in charge that will drive that change - and I'm not convinced that anybody in the current setup is committed to that fundamental altering of the way we do policing."
Other deputies have, however, been stronger in their criticisms of the Commissioner.
The Solidarity-People Before Profit group is preparing a separate motion of no confidence in Noirín O'Sullivan.
Solidarity TD Paul Murphy suggested Commissioner O'Sullivan's position is "even more" untenable after the update provided yesterday.
PBP's Richard Boyd Barrett said: "It is beyond belief that Noirín O'Sullivan can say, even if the Dáil votes no confidence in her, she intends to stay where she is and there's nothing the Dáil can do about it.
"That is an affront and insult to democracy," he added.
