Aer Lingus management and the cabin crew union IMPACT have accepted an invitation to talks at the Labour Court on Wednesday in a bid to avert two further one-day strikes at the airline next week.
The Labour Court issued the invitation this afternoon.
IMPACT sources said the union would not be calling off the strikes ahead of the talks.
Aer Lingus earlier said it would attend the Labour Court meeting.
The airline has stopped taking bookings for 16 and 18 June, when the strikes are due to take place.
The dispute centres on rosters, which the cabin crew say are erratic, exhausting and make family life difficult.
Minister for Transport, Tourism and Sport Leo Varadkar had accused Aer Lingus management and cabin crew of engaging in "megaphone diplomacy" in their row over rosters.
Mr Varadkar urged them to take the dispute to the Labour Relations Commission.
The threatened strikes will disrupt the travel plans of up to 70,000 passengers.
Mr Varadkar said he was concerned about the prospect of further strikes causing huge inconvenience to passengers.
He said essentially this was a dispute over rosters, which would ultimately be solved through negotiation.
He said "megaphone diplomacy" involving threats of strikes on one side and threats of redundancies on the other were not serving anyone's purpose.
Mr Varadkar said if management and cabin crew could not resolve their differences through bilateral talks, they should go to the LRC to try to broker a compromise.
Aer Lingus had been expected to make an announcement today or tomorrow to confirm to passengers what arrangements it is making in light of the strike threats.
Both sides still dispute who is to blame for the escalation of the row.
Aer Lingus insists that it merely adjourned talks for the evening on Friday, and was shocked when later that evening the strikes were announced.
However, IMPACT has accused the airline of dumping a "take it or leave it" ultimatum on them.
Over the weekend, Aer Lingus' Chief Executive, Christoph Mueller, wrote to staff saying their job security is being damaged by the day.
He said 150 potential new jobs at the airline may be lost if there is further industrial disruption.
Meanwhile, the expert panel seeking to resolve the intractable dispute over the IASS aviation pension scheme is due to report on Friday.
Observers fear that that could trigger even more widespread industrial action in both Aer Lingus and the Dublin Airport Authority.