The threat of further strike action at Aer Lingus could affect up to 80,000 passengers.
Friday night's talks between IMPACT and management over an ongoing roster dispute ended without any resolution with strike action by cabin crew looks likely.
Staff at the airline are threatening to down tools on June 16 and 18.
Staff are seeking a rota of five days on and three days off in an ongoing row over rosters.
The Minister for Transport, Leo Varadkar, encouraged both sides to use the existing third-party methods of resolving the dispute.
"The possibility of further industrial action at Aer Lingus is a matter of grave concern," he said.
"The State's industrial relations machinery remains available to both sides and should be utilised, if direct negotiations have proved unsuccessful. This dispute can and will only be resolved through negotiation."