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 1 August for full implementation of cost-cutting proposals.
SIPTU, which says its officials had nothing to do with the stoppage, says change will only be implemented by agreement.
In a letter to the SIPTU President, Jack O'Connor, chief executive of the airline, Dermot Mannion, accused staff who stopped working without prior notice of showing complete disregard for customers.
Aer Lingus 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 describes Saturday's events as a serious and very worrying development in the Aer Lingus-SIPTU relationship.
On 1 June, the board of Aer Lingus approved the purchase of $2.4bn worth of new aircraft - provided management's cost savings are implemented.
In separate correspondence to senior officials in SIPTU and IMPACT, he has set a deadline of 1 August for finalising that cost-cutting programme.
However, unions remain adamant that change can only be implemented by agreement.
