The Public Accounts Committee is considering moving forward Garda Commissioner Nóirín O'Sullivan's next appearance at the committee, chairman Seán Fleming has said.
Ms O'Sullivan was originally planned to appear before the committee again in July, but this may now be brought forward in light of new documents provided to the committee on Templemore.
The documents raise fresh questions over the Garda Commissioner's account of a key meeting about finances in the Garda College in Templemore.
Ms O'Sullivan told the committee last week that she first learned about the problems at the training college in a very brief exchange with the director of Human Resources at An Garda Síochána.
However, John Barrett contradicted her and said the meeting lasted over two hours. He has provided paperwork to support this.
During Leaders' Questions, the Taoiseach said that Ms O'Sullivan retains the confidence of the Government.
He was responding to Fianna Fáil leader Micheál Martin, who said revelations about the financial irregularities at Templemore Garda College demanded urgent action by the Government.
"This is stretching the credibility of the force to its very limit, and with it the Government's as well," Mr Martin said.
He said the Garda Commissioner had a legal obligation to inform the Minister for Justice about the irregularities under Section 41 of the Garda Síochána Act.
"Do you accept that the commissioner did not discharge her legal obligations to inform the minister of matters which would affect public confidence in An Garda Síochána?" he asked.
"It took 15 months ... Do you think that's good enough? ... Do you still have confidence in An Garda Commissioner to manage her duties?"
In response, Enda Kenny said he agreed that it is absolutely critical that people in the State have faith and trust in An Garda Síochána.
"I have faith in the Ccommissioner to do her job ... These matters are being investigated by the Public Accounts Committee, the C&AG, and the Policing Authority".
He said Section 41 is a section of the act that enables a commissioner of the day to send Section 41 notices to the minister of the day, and "that is a matter of judgement for the commissioner of the day".
"The Government retain confidence in the Garda Commissioner, it would be a mistake to personalise issues looking at the structure", he said.
But Mr Martin said the act did not enable a commissioner to make a report to the minister, it obliged her to do so, he said.
"The thing is completely untenable and unacceptable" he said. "It is time you acted."
The Sinn Féin leader asked the Taoiseach twice during Leaders' Questions whether he had confidence in Ms O'Sullivan.
Gerry Adams asked if Mr Kenny could imagine a "poor" or "powerless" person getting away with a "smidgen" of what has happened.
The Taoiseach said it was "quite a number of years since the events took place", adding that it was only "right and proper" that the truth and facts about the matter be found out.
He said that is why the Public Accounts Committee was investigating the issue of Templemore and that the Policing Authority was overlooking recommendations sent to it.
The Taoiseach said it took time "for these things to evolve so the culture will change and it's seen by the people of the country".
He also added it was right that Mr Barrett's report be examined by the PAC which he said was entitled to produce a report and findings.
However, he said he would like to see the PAC doing its job on 13 July and see the Garda Commissioner answer charges that Mr Adams made in the Dáil this afternoon.
Mr Adams put it to the Taoiseach that all was not well and said it was a "wonderment" to him that the Government has not removed Ms O'Sullivan from her position.
He suggested that the instinct of the Government was to protect the establishment and "not move" unless it is forced to take action.
Minister for Justice Frances Fitzgerald earlier said that at the end of the day it is the Garda Commissioner's decision whether or not to refer an issue to her.
The Tánaiste was responding to questions from journalists as to whether she thought she should have received a referral on the issues surrounding Templemore after the garda head of legal affairs advised Commissioner O'Sullivan to make such a referral.
Ms Fitzgerald said the commissioner has to make decisions on a daily basis and gets legal advice on many issues.
She said she has confidence in Ms O'Sullivan who is implementing change in an organisation that needs change.
She also described the issues surrounding Templemore as extremely grave and serious.