Some teachers and gardaí have been warned they will lose pay increments from Friday.
The warning comes ahead of the Lansdowne Road pay deal formally taking effect from July 1st.
The ASTI and two Garda associations have both refused to sign up to the deal which will see partial pay restoration.
Public Expenditure Minister Paschal Donohoe says the Government must be loyal to the unions who accepted the deal.
"We have to follow the law in this area, and the law lays out a process in relation to what will happen if unions don't want to be part of the Lansdowne Road agreement," he explained.
Meanwhile, the ASTI Standing Committee says it has accepted an invitation from the Education Minister Richard Bruton to discuss 'issues of concern'.
The committee will also issue a directive for union members to withdraw from the Croke Park hours.
ASTI President Máire G Ní Chiarba said: “Teachers have experienced a significant deterioration in their working conditions in recent years.
"Young and newly qualified teachers have been disproportionately affected due to the introduction of new pay scales and new pension arrangements. Many of these teachers are unable to obtain secure employment and do not earn a full salary," she added.
68% of the union's members voted to withdraw from the existing Croke Park hours.
The Garda Representative Association (GRA) earlier said it is considering industrial action, and that it will not re-enter talks on the Lansdowne Road Agreement.
