Updated at 18:12
The Government said they are considering a full "root and branch" review of An Garda Síochána.
The Garda Commissioner is currently facing a motion of no confidence from a number of political parties after a series of scandals hit the force.
The Government received a detailed briefing from the Tánaiste this morning on the recent revelations regarding the Garda handling of matters relating to Mandatory Alcohol Testing and Fixed Charge Notices.
The statement from the Government said "There was a consensus in that discussion that these revelations have given rise to the most serious concerns, not just among public representatives but also the general public."
"It is a matter of great importance to our country that the Government, the Oireachtas and all citizens can trust members of An Garda Síochána to carry out their duties fairly and impartially, and in accordance with the law.
"It is crucial that the public can believe statistics and other information provided by An Garda Síochána.
Process of reform
"It is absolutely essential that a process of reform is rigorously implemented in An Garda Síochána, and that it is seen to be implemented, including through close oversight by the Policing Authority.
"The Government has introduced a range of important reforms to policing in the State in recent years, including the establishment of a Policing Authority, additional powers for GSOC, greater civilianisation and open recruitment and the provision of significant extra resources.
"The Garda Commissioner has also instituted a significant programme of internal reorganisation and reform, which is being overseen by the Policing Authority and the Government also restates its confidence in the Commissioner today.
Public concern
"A series of unacceptable revelations about the operations of the Gardaí continue to emerge, with the Mandatory Alcohol Testing and Fixed Charge Notices being the latest.
"Notwithstanding any internal review the Government believes that an external investigation into these two specific matters needs be carried out.
"The Government believes the level of public concern is now so profound that it may now be time to conduct a thorough, comprehensive and independent root-and-branch review of An Garda Síochána.
"That is clearly a proposal that will require further detailed consideration by the Government."
The statement concluded with "Government also believes that any such proposal should command widespread support in the Oireachtas and accordingly be the subject of consultation with the Opposition, and ultimately approval by the Oireachtas."
Clare Daly, an Independents-4-Change TD for Dublin & Fingal says that people need to be held accountable, rather than a root and branch review.