The Association of Garda Sergeants and Inspectors has warned that any cuts to discretionary overtime must not impact on core policing.
Garda Commissioner Drew Harris has warned that the force is set to significantly exceed its budget for this year.
Warning that this is "not a sustainable position" he has announced plans to cut discretionary and administrative overtime.
Rank-and-file gardaí have already warned that the decision could prevent members on the frontline - especially those involved in the fight against organised crime - from doing their job effectively.
On The Pat Kenny Show this show this morning, the general secretary of the Association of Garda Sergeants and Inspectors (AGSI) John Jacobs said members want time to consider the commissioner's plan before it is enforced.
"Well I think we need to examine it closely and we have not had a chance yet as an association to examine what the commissioner has issued," he said.
"But we need to be sure that the cut in overtime does not impact on core policing service - which do not impact on overtime."
Overtime
In his statement, Commissioner Harris said overtime will still be available for "specific policing and security operations" - but only where it is approved by the deputy commissioner for policing and security.
"An Garda Síochána must work within the annual budget provided to it by Government," he said.
"This has been stressed continually to Garda managers at all levels throughout 2018."
The cuts were made in response to new figures showing that the force's overtime bill has already hit €84.7m - meaning there is only €15.3m available for the remainder of the year.
"Extraordinary development"
Yesterday, the Garda Representative Association described the move as an "extraordinary development," insisting overtime is "only ever incurred where necessary."
Spokesperson John O'Keefe said: “The agreed overtime must now be reinstated if we are to keep our streets safe in the lead up to Christmas."
He said authorities should remain conscious of the signal the decision sends to criminal elements ahead of the festive season.