The Garda Commissioner is facing increased pressure to consider her position after Fianna Fáil said it cannot express confidence in her at this time.
Tonight, Sinn Féin said it would publish a motion of no confidence in Noirín O'Sullivan tomorrow after it emerged that more than 14,500 people who were prosecuted for road traffic offences are to have their convictions quashed because of garda error.
It was also revealed that from 2011 to 2016, the number of drink-driving tests gardaí claimed to have carried out was hugely exaggerated, by over 937,000.
Speaking on RTÉ's This Week, Mr Martin said his party cannot express confidence in the Commissioner O'Sullivan, but does not want to embroil Dáil Éireann in the controversy.
Mr Martin said he wants a clear statement from the commissioner to explain why the Policing Authority was not told about the controversy until recently.
He said: "We can no longer articulate confidence in the Garda Commissioner or indeed at this particular point in time in the administration of justice, until we get absolute clarity in plain language as to what happened here."
Yesterday, the commissioner said the revelations over penalty points and garda breath test discrepancies are "totally unacceptable and not in keeping with the standards of a modern and professional police service".
Mr Martin said there needs to be a "radical change in terms of how policing is managed in this country".
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He also said the patience and credibility of the An Garda Síochána has been "seriously undermined by these revelations".
He said his party has not been satisfied by the response of the commissioner, An Garda Síochána, or the Minister for Justice to this crisis.
Mr Martin added it was "untenable and unacceptable" that the policing authority was not informed of the revelations officially and learned of them from the media.
Meanwhile, the Minister for Social Protection Leo Varadkar has reiterated that the Government has confidence in the Garda Commissioner but he said in light of what has been said by some Independent ministers and the leader of the opposition they will discuss this further at Cabinet on Tuesday.
Mr Varadkar said the revelations they have seen in the last couple of days really are not acceptable and are appalling.
But he said that the Government's view is that the Commissioner is part of the solution and she has put in place the two solutions to these problems in the last couple of months.
He said he did not think she should consider her position at this time and that the Government has confidence in her.
Earlier, Minister for Agriculture Michael Creed said there is nothing to suggest the commissioner is implicated in the latest revelations about the force.
Speaking on RTÉ's The Week in Politics, the minister said the commissioner deserves support and nothing would be served by delivering a head on a plate.
Independent Alliance TD and Minister of State John Halligan said he personally believes that Ms O'Sullivan should consider stepping aside.
Speaking on RTÉ's This Week programme, Mr Halligan said that "controversy after controversy" is doing irreparable damage to the garda force.
He said that he thinks it is losing credibility as a result.
He continued that the Independent Alliance will meet on Tuesday to discuss the matter and will then collectively issue a statement.
Fianna Fáil TD Niamh Smyth said the commissioner had failed to provide any credible explanation for the revelations.
Deputy Smyth said Fianna Fáil will give Commissioner O'Sullivan just "next week" to provide a clear explanation, and then the party would review its position on her.
Minister Creed said he expects the commissioner will come before an Oireachtas Committee very soon to provide detailed answers.
Garda Commissioner deserves support from Govt @creedcnw tells #twip pic.twitter.com/EcEu88MxnA
— The Week in Politics (@rtetwip) March 26, 2017
However, Sinn Féin's Martin Kenny said the commissioner must step down because the public had lost trust in An Garda Síochána.
Sinn Féin calls for Garda Commissioner to step down @Martin_Kenny #twip pic.twitter.com/ZAx6SVeo53
— The Week in Politics (@rtetwip) March 26, 2017
Fianna Fáil calls for Garda Commissioner to give a “clear explanation for what has happened” next week @NiamhSmythTD #twip pic.twitter.com/uyooXH2eIl
— The Week in Politics (@rtetwip) March 26, 2017