Aer Lingus and the Irish Air Line Pilots' Association (IALPA) have been invited by the Labour Court to attend separate meetings tomorrow over the pilot pay dispute and both sides have accepted.
Despite the court's intervention, industrial action is still due to begin later this week.
Over the weekend, Aer Lingus confirmed that at least 220 flights have been cancelled from Wednesday until Sunday.
The airline previously announced 124 cancellations resulting from a work-to-rule.
In a statement this evening, Aer Lingus said it had received a request from the Labour Court to provide a briefing on the pilot pay dispute.
"Aer Lingus has confirmed that it will attend the meeting. Aer Lingus understands that Fórsa has received a request to attend a separate meeting with the court," it said.
IALPA is a branch of the Fórsa trade union.
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The Taoiseach has welcomed the decision by both sides to attend the meetings.
Simon Harris met employer and union representative bodies today to discuss a range of economic issues.
He said that given the "unique" nature of the Aer Lingus dispute, it is important that it is resolved as quickly as possible.
Mr Harris urged those present to do all they could to get people back to talks to resolve the matter quickly and to avert any further disruption and distress for families.
"These meetings provide an opportunity to try make progress and ensure the travelling public are not further affected by this dispute," he said.
Earlier, the Tánaiste described as "shocking" the degree to which the needs of the Irish travelling public were being ignored by both sides in the dispute.
Micheál Martin appealed to IALPA and Aer Lingus management to "get around the table" on the basis of the existing Labour Court recommendation.
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Thousands of passengers intending to travel with the airline over the coming week face huge uncertainty, with pilots set to begin their indefinite work to rule from Wednesday.
Speaking in Luxembourg, where he attended a meeting of EU foreign ministers, Mr Martin said: "I think it is shocking the degree to which the needs of those who travel are being, in my view, ignored in the context of this dispute.
"There's only one way to resolve this, it's through negotiations and getting around the table. It is that simple by the way, and all disputes end, and the most effective way that they end is by utilising the industrial relations machinery that we have available in the State, which is the WRC (Workplace Relations Commission) and the Labour Court.
"The Labour Court did issue a recommendation, an interim one, which does form the basis, in my view, for further negotiations.
"I would appeal to both sides to get around the table and to think of the many thousands of families and workers across the country. This is the one time in the year that they get an opportunity to travel for their holidays. They've planned for these, they've saved for these - it's shocking that they're being ignored, and wilfully, if you like, put to one side in this battle between the management of Aer Lingus and unions."
Mr Martin said there was an obligation on Aer Lingus to make every effort to create momentum around talks and getting around the industrial relations table to get an agreement hammered out.
IALPA seeking 24% pay increase
Yesterday saw both sides in the Aer Lingus pay dispute accuse of each other of refusing to engage.
In a statement earlier today, Aer Lingus said it wrote to IALPA yesterday requesting "meaningful direct discussions" to try and resolve the dispute, and to discuss improvements in productivity and flexibility.
"The airline has repeatedly sought to engage directly with IALPA on ways to increase pilot pay beyond the 12.25% increase agreed with all other collectively bargained groups, based upon reaching such agreement on improvements in productivity and flexibility. IALPA has informed Aer Lingus that is has no mandate to enter into such discussions," the statement said.
"As such, at this point no direct discussions have been scheduled. Aer Lingus has also informed IALPA / FORSA of the airline's availability to re-engage with the industrial relations framework of the State (the Labour Court and the Workplace Relations Commission) - at this point, this request has also been rejected by IALPA / FORSA."
IALPA has said that the 24% pay increase it is seeking for its members is based on cumulative inflation over recent years and that its members should not have to pay for their salary increase by agreeing to work practice changes.
President of IALPA Captain Mark Tighe said the group is willing to talk with Aer Lingus but added that preconditions are not acceptable or helpful.
"The company have said in media all through the week that they are looking to meet. We have shown that not to be the case," he told RTÉ's Drivetime.
"However, yesterday, they did come back to us in writing saying that they would meet, and they set pre-conditions for that meeting.
"We wrote back to them and said ... preconditions are not acceptable within an open negotiation, however we still will happily meet ... and we have not heard from them yet."
Capt Tighe said Aer Lingus wanted any increases in payment over and above what they are offering to be financed by working conditions on a euro-for-euro basis.
"What they are actually asking us to do is pay for our pay increase, and obviously, that is not acceptable," he said, adding that they have been seeking a reasonable accumulative inflationary increase over the past five years.
He said they were not looking to increase their pay, merely maintain it.
Explained: Customer rights if your flight is cancelled
Over the weekend Aer Lingus confirmed that at least 220 flights have been cancelled from this Wednesday to Sunday.
The airline previously announced 124 cancellations resulting from a work-to-rule which begins on Wednesday.
Ryanair has announced that it has added extra flights to/from London Stansted, Malaga and Faro airports on 29 and 30 June in response to the strikes, which it said had caused many Ryanair flights to be sold out to these destinations next weekend.
The airline said that contrary to what it described as some false social media claims, Ryanair has not increased its fares in response to the dispute.
The company said it is working closely with Aer Lingus to accept some of transfer passengers, but added that it has very limited seat availability.
"We are working with Aer Lingus to assist disrupted passengers where we have seat availability, and we have also offered Aer Lingus some wet lease capacity over the coming days, if that will assist them to help disrupted passengers during these regrettable and unnecessary pilot strikes," said Ryanair's Chief Marketing Office Dara Brady.
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Meanwhile, hoteliers warned the disruption to Aer Lingus flights poses a serious risk to tourism.
President of the Irish Hotels Federation Michael Magner,called on both parties in the dispute to meet as a matter of urgency and come to an early resolution.
"There is enormous concern throughout our industry given how important Aer Lingus is for inbound visitors, particularly for transatlantic and long-haul flights.
"We are already seeing hotel cancellations as guests change their holiday plans, and there is a risk that this pattern of cancellations could escalate over the coming days."
Additional reporting Tony Connelly
