Aer Lingus has threatened to take disciplinary action against staff who staged an unofficial stoppage last Saturday causing disruption to thousands of passengers.
It has also set a deadline of August 1 for full implementation of cost-cutting proposals.
SIPTU, which says its officials had nothing to do with Saturday's stoppage, says change will be implemented only by agreement.
In a letter to SIPTU president Jack O'Connor, Aer Lingus chief executive Dermot Mannion accused staff who stopped working without prior notice of showing complete disregard for customers.
The airline is mounting an investigation into the organisation and execution of the stoppage, and has warned it could lead to disciplinary action. Pay will also be docked from relevant workers.
Mr Mannion described Saturday's events as a serious and very worrying development in Aer Lingus's relationship with SIPTU.
But the union states categorically that none of its officials were aware of or engaged in organising the stoppage.
On June 1, the board of Aer Lingus approved the purchase of $2.4 billion worth of new aircraft, provided management's cost savings were implemented.
In separate correspondence to senior officials in SIPTU and IMPACT, Mr Mannion has set a deadline of August 1 for finalising that cost-cutting programme.
