Fianna Fáil has joined other opposition calls for the Garda Commissioner to resign but the Taoiseach and Justice Minister have said they support her.
Fianna Fáil's justice spokesperson said his party believes the best option for Garda Commissioner Nóirín O'Sullivan is for her to resign.
Speaking to RTÉ News, Jim O'Callaghan said it is clear when Fianna Fáil say they do not have confidence in her, which has been the case since the controversy on breath tests and wrongful convictions emerged.
Referring to yesterday's Oireachtas Public Accounts Committee meeting and the contradiction in accounts of a meeting involving Ms O'Sullivan and senior garda management, he said a State agency should be able to supply the public with a consistent and accurate account of what happened.
Speaking on RTÉ's Six One News, Mr O'Callaghan acknowledged that Commissioner O'Sullivan was proper in the actions she took subsequent to the meeting with the Director of Human Resources, but he said it was not satisfactory for two senior officials to be inconsistent and inaccurate in their accounts of what happened.
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The Commissioner was questioned by the committee on financial irregularities at the Garda College in Templemore.
An internal garda audit showed poor financial management, a large number of bank accounts, and thousands of euro spent on entertainment, presentations, sponsorship and donations to charity.
A garda spokesman said that An Garda Síochána is making no comment in reaction to Mr O'Callaghan's remarks.
However, a spokesperson said that gardaí are currently implementing a programme of modernisation and renewal, and issues like this will arise and will be dealt with.
Speaking in Canada, Taoiseach Enda Kenny expressed his full confidence in the Garda Commissioner.
He said: "I don't have the details of any evidence given by the Garda Commissioner to any committee yesterday. I still retain full confidence in her to do her job and expect her to do that.
"I would point out we have put in place the Independent Policing Authority, GSOC with enhanced powers, an independent garda inspectorate and the Minister for Justice is very anxious to see that every week measures are taken that will deal with the many challenges that An Garda Síochána face."
Meanwhile, a spokesperson for the Tánaiste and Minster for Justice Frances Fitzgerald has said that she will not be seeking Commissioner O'Sullivan's resignation.
The spokesperson said that Ms Fitzgerald's position remains "unchanged" and she "retains confidence" in the Commissioner.
O'Sullivan defends handling of financial issues
Earlier, Ms O'Sullivan defended her handling of issues relating to the financial irregularities at the Garda College in Templemore.
Ms O’Sullivan was addressing the media after being questioned on the issue by the PAC yesterday.
Among the findings in the internal garda audit, was that over €124,000 which was collected from land owned by the Office of Public Works that was bought but never used for a tactical training centre.
She said the issues at Templemore were legacy matters dating back 30 years which she only became aware of in 2015.
Ms O'Sullivan said that when she did become aware of the issues she acted promptly.
She also said the auditor has still not finished his work and an Assistant Commissioner has been appointed to investigate the controversy. She is due back before the PAC in July.
Yesterday the head of An Garda Síochána's internal audit system, Niall Kelly, told the PAC he believes he was "duped" when he was told action would be taken in relation to financial irregularities at Templemore.
This afternoon Ms O'Sullivan insisted she had not misled the committee.
Labour TD and PAC vice chairperson Alan Kelly described yesterday's meeting as "unbelievable" and "nothing like he had ever seen in his political career".
"I specifically asked every witness when did they first know about Templemore. The Commissioner said she first knew of any irregularities in Templemore in July 2015.
"A couple of witnesses came forward, including one who was a member of the administration team who said that they were aware before.
"Most others said they weren't actually aware. The Department of Justice said that they weren't aware up until the report coming into them which actually was in 2016," said Mr Kelly.
Speaking to RTÉ News, Mr Kelly said that the Labour Party has consistently called for the resignation of Commissioner O'Sullivan.
He said: "I do not have confidence in Nóirín O'Sullivan to be the Commissioner of the gardaí, and believe she has to step down. What happened yesterday in the PAC absolutely confirms that view to me."
Sinn Féin's David Cullinane, who is a member of the PAC, said that the contradicting evidence given at the committee yesterday has made the Commissioner's position "untenable" and called on her to resign.
He said: "Ms O'Sullivan's position is not tenable and she should resign immediately. If she does not then Minister Fitzgerald must intervene."