Aer Lingus management and the trade union IMPACT have accused each other of not being prepared to negotiate over cabin crew rosters.
IMPACT, representing cabin crew at Aer Lingus said the threatened strike action could be averted but the company will have to act fast.
Bernard Harbor of IMPACT said his union wanted to continue negotiations through the weekend.
However, the airline said it was engaging with the union and does not understand why IMPACT said the talks collapsed.
Mr Harbour added that IMPACT would accept an invitation to talks at the Labour Relations Commission if one is extended
Aer Lingus has said that two days of strike action threatened for the week after next will disrupt thousands of passengers as the peak holiday season starts.
IMPACT, which represents cabin crew, has called for strikes on 16 and 18 June.
Aer Lingus Director of Communications Declan Kearney said that the threatened action could disrupt around 80,000 passengers.
He said the airline had reached agreement with crew over rostering issues as requested, and so was unsure as to what cabin crew were demanding now.
He said he was perplexed and at a loss as to why IMPACT had said that talks had collapsed.
The airline understood they would resume next week and that it only learned of further strike action through the media, he added.
Minister for Transport, Tourism and Sport Leo Varadkar said 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," he added.