Minister for Transport Leo Varadkar has said that he is concerned that former garda commissioner Martin Callinan knew of unlawful recordings in November and did not tell the Minister for Justice at that point.
Mr Varadkar said an internal investigation was set up rather than informing Alan Shatter as the former commissioner should have done.
He added that there had "even been inquiries about destroying the tapes".
Mr Varadkar said that this was much more of an issue of concern than anything else.
He said he has full confidence in Mr Shatter and that the "opposition had got it all wrong".
He said that "instead of making political capital" and attacking Mr Shatter, they should be asking why gardaí did not inform the Government earlier.
However, sources close to Mr Callinan have said that the former commissioner never considered destroying any tapes or recordings of phone conversations.
The sources say that the former commissioner sought legal advice on the tapes because the Data Protection Act requires material to be destroyed once it is no longer needed and some of the recordings date back to the 1980s.
On legal advice, the sources say the former commissioner wrote to the Data Protection Commissioner, who advised that in this instance the recordings were not to be destroyed.
The sources were commenting in response to comments by Mr Varadkar this morning.
The sources also say that, while they would not comment in detail as to the content of the conversation between the Secretary General of the Department of Justice and Mr Callinan on Monday night of last week, the possible destruction of any recordings was not discussed at all.
Mr Callinan wrote to the Department of Justice at the beginning of March about the recording and retention of telephone conversations in garda stations.
In a letter to the secretary general of the department, Mr Callinan asked that Mr Shatter be informed of details of the recordings.
In the letter he also says that he consulted with the Attorney General on 11 November 2013.
The letter, entitled 'Recordings of Telephone Conversations made and retained in Garda Stations', says the recordings, which are now in court proceedings, took place in the 1990s.
They are of members of the Garda Síochána and members of the public.
The former commissioner said the systems were set up in the 1980s to enable gardaí to record calls to and from control rooms; in particular 999 calls, bomb threats and other messages.
The practice continued in some stations over the years with recordings retained in the garda stations.
The original recording systems were replaced by dictaphones during the 1990s and by another system in 2008.
In the letter, Mr Callinan also says that he directed that routine recording of non 999 calls to garda stations cease and confirmed in the letter to the department that all recordings except 999 calls ceased nationally on 23 November 2013.
The total number of tapes is over 2,400 and Mr Callinan says in the letter that he consulted with the AG and expected to consult with the Data Protection Commissioner.
Mr Varadkar was speaking at an event to mark the removal of the €3 air travel tax from tomorrow.
Gilmore 'surprised' dept did not inform Shatter sooner
Tánaiste Eamon Gimore has said it is "surprising" that the Department of Justice did not inform Mr Shatter of the garda telephone recordings until two weeks after it received a letter from the former garda commissioner.
Mr Gilmore said this would be one of the issues examined by the Commission of Investigation that is to be set up into the affair.
He said the substance needed to be dealt with and he took it very seriously.
The Labour leader was asked if the Attorney General should have brought the issue to the Cabinet's attention back in November when Mr Callinan first raised it with her office.
Mr Gilmore said Máire Whelan informed the Taoiseach when she became aware of the "scale and significance" of the recordings involved.
Call for dept officials to appear before Justice C'ttee
Independent TD and Oireachtas justice committee member Finian McGrath has asked the chairman of the committee to invite the Secretary General and senior staff from the Department of Justice to attend the committee to answer questions about the letter.
Elsewhere, Sinn Féin's Justice Spokesperson and committee member Pádraig Mac Lochlainn said that Mr Shatter should clarify his knowledge of the Ian Bailey case going back to November 2011 up to Monday and Tuesday of last week.
He told RTÉ’s News at One that the Attorney General should make a statement clarifying her involvement in this matter since last November and the former garda commissioner should make a public statement on the matter.
Minister for Education Ruairi Quinn has insisted Mr Shatter has his full confidence, but that he did not have enough information to say whether he handled the current controversy well.
Describing Mr Shatter as a diligent and attentive minister, Mr Quinn said it would be premature to make any detailed comment ahead of the proposed commission of inquiry.
However he told journalists at the launch of an anti-bullying initiative aimed at parents that he was surprised at the Department of Justice's delay in passing on a key letter to the minister.
Meanwhile, Minister for Jobs, Enterprise and Innovation Richard Bruton said Mr Callinan was not asked to quit and made his decision "on his own grounds".
He said Government was trying to "fix" problems dating back a number of years and the proposed Commission of Investigation would aim to help do this in relation to the recordings issue.
He said the hope was to emerge with a much stronger system, a modern police authority and stronger protection of whistleblowers.