Attorney General Maire Whelan and senior officials in the Taoiseach's department are scrutinising a dossier of cases of mismanagement by the gardai – some involving murder, abduction and assault.
Justice Minister Alan Shatter's officials are also understood to be trawling through department records to establish how he dealt with the allegations, when they were originally sent to him by garda whistleblower Sergeant Maurice McCabe.
The garda crime investigation allegations include 10 cases over the years 2007-2009.
Mr Shatter is expected to issue a response today to claims that he failed to act on the information for two years.
Meanwhile, Mr Kenny has given a personal pledge to deal with allegations that the gardai failed to properly investigate serious crimes including kidnap and murder.
The Taoiseach has got the Attorney General's office and some of his most senior officials examining the documents.
"The documents are being studied very seriously. The Attorney General is involved," a government source said.
The Labour Party wants a response on the issues within the next 24 hours. Sources say the party is not prepared to wait until next Tuesday's cabinet meeting for a response.
The Taoiseach said: "I have no intention of playing politics with an issue as serious as this. I'll deal with it, and we'll deal with it, in the interests of our State, our country and of our people."
But Mr Kenny has not said whether he will yield to increased opposition calls for an independent commission of inquiry.
And he has made no comment on claims that the Justice Minister had a dossier of these serious allegations for the past two years – but failed to do anything about them.
Last night, Mr Shatter admitted he sacked the special confidante, whose role was to receive allegations of wrongdoing from gardai, because he didn't deny an alleged conversation with Sergeant McCabe.
Confidential Recipient Oliver Connolly was sacked on Wednesday after a transcript of a conversation emerged, and was read into the Dail record, in which he told Sgt McCabe that Mr Shatter will "go after you".
Mr Shatter said if the conversation had taken place, then Mr Connolly's actions had "undermined the office of the Confidential Recipient".
"Contacts with Mr Connolly over the following two weeks did not satisfy me as to his response to the controversy.
"I informed him that in the context of his failure to unequivocally repudiate the content of the alleged conversation or take the necessary action to restore public confidence in the office of Confidential Recipient, I believed his position was untenable and I had no alternative but to relieve him of the position."
Mr Shatter had already intended to abolish the role. New legislation, now going through the Dail, will allow garda whistleblowers to go directly to the Garda Ombudsman.
There were very angry scenes in the Dail yesterday during which the opposition increased pressure on the Government and the Justice Minister who was in Greece at an EU meeting.
Mr Martin added to allegations made late last week and again on Wednesday. He said he had been handed additional material yesterday and also passed it to the Taoiseach.
The Fianna Fail leader told the Dail the allegations related to shocking cases, which included abduction and murder.
It has emerged that the allegations include issues regarding the handling of Jerry McGrath, who murdered Sylvia Roche Kelly in Limerick in 2007. The murder investigation is not the focus of controversy.
But allegations have been made regarding the handling of McGrath in the lead-up to the murder – he had been charged with several crimes and was on bail at the time.
Mr Martin called for a comprehensive statement from the Justice Minister on these issues, and on the decision announced on Tuesday to sack the confidential recipient, Oliver Connolly.
John Downing and Fionnan Sheahan