The Irish Airline Pilots' Association has accepted an invitation to talks with Aer Lingus tomorrow, with industrial action to continue in the meantime.
The airline issued a fresh invitation to IALPA today in a bid to resolve the ongoing pay dispute.
A spokesperson for the Taoiseach said he welcomed the move and added he "has been clear this dispute is having a disproportionate impact on the travelling public".
"All disputes are resolved by compromise and negotiation. The Taoiseach urges both sides to engage in good faith to resolve this dispute," the spokesperson added.
Aer Lingus has said that there are no additional cancellations so far resulting from an indefinite work-to-rule by pilots which began at midnight.
The industrial action involves IALPA members not working overtime or any other out-of-hours duties requested by management.
They are also refusing to log on to Aer Lingus online portals outside of work hours or answer work phone calls outside of work hours.
Aer Lingus has so far cancelled 270 flights because of the work-to-rule and a planned eight-hour strike on Saturday.
The President of IALPA has said the union would not be suspending its work-to-rule pending the talks.
Speaking on RTÉ's Drivetime, Mark Tighe also IALPA would not commit to to not escalating the dispute further while the Labour Court reviews the situation in July.
He said Aer Lingus is "under-crewed" and the result of that pilot shortage is the number of flight cancellations the airline is imposing during the industrial action.
"The extent of the cancellations would be to do with how the company is being managed," he said.
"Obviously a work-to-rule will have an effect, but most pilots, the vast majority, don't actually work on their days off... the some pilots that do work on their days off, which they're perfectly entitled to, are now not - it doesn't add up," he said.
He defended the pilots' claim of a near 24% pay increase, calling it "fair and equitable" and said he could not speak to how Aer Lingus cabin crew and other staff negotiated an increase of around 13%, and "what it was they asked for."
However, he said the other Aer Lingus staff that are represented by different unions are "highly supportive" of the pilots, including a formal letter of support from the cabin crew union.
He said Aer Lingus' parent company, IAG, has already "stood over an increase in excess of 24% of total pay to our colleagues and pilots in British Airways, so this has already happened in IAG."
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(Listen: Kieran Dineen talks to Aer Lingus passengers at Dublin Airport this morning)
Aer Lingus Chief Corporate Affairs Officers Donal Moriarty said the airline was very disappointed that so many customers have been impacted so far.
"However, the cancellations that we've implemented have provided resilience and has protected the services that we are progressing with," Mr Moriarty said.
"So far, it is being managed as well as can be expected and we would hope to continue in that vein," he added.
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The Chief Executive of the Irish Travel Agents Association, Clare Dunne, said the news that Aer Lingus and its pilots are to meet tomorrow morning is a positive development in the pay dispute.
After the "crushing disappointment" of the Labour Court's determination that it could not do anything at this time, she said this move "is absolutely cause for optimism and for hope..."
She said it was really important that the two sides "leave their baggage outside the door":
"There's absolutely no point in going in making it seem like they're going to talk if they're not actually going to sit down in a spirit of good will, listen to each other, and make up their minds to find a solution to allow both sides to get back to what they should be doing, which is looking after customers."
Read more: Aer Lingus halts pilot perks due to industrial action
IALPA and Aer Lingus management attended separate meetings at the Labour Court yesterday in a bid to resolve the dispute but the court advised both parties that it would not be intervening at this time and would review the matter in July.
Aer Lingus has warned that further, last-minute disruptions may occur over the coming days and that it is possible that passengers may find out their flight is cancelled while they are at the gate waiting to board.
Yesterday, the airline expressed disappointment that the Labour Court would not be intervening.
"Aer Lingus has made it clear that it remains available for discussions both directly and through the State's industrial relations framework," the airline said.
"Aer Lingus will continue to focus on minimising the disruption caused to customers by IALPA's industrial action," it added.
IALPA said it noted the decision of the Labour Court not to intervene and that it remained available to re-enter meaningful negotiations.
In recent days, each side has accused the other of refusing to meaningfully engage.
Aer Lingus has said that agreements on flexibility and productivity would have to form part of any improved pay offer.
IALPA said however that the 24% pay increase it is seeking reflects cumulative inflation over recent years and should not be linked to work practice changes.
Sinn Féin calls for Government intervention
Minister for Finance Michael McGrath has said the dispute is "a very serious situation" and is damaging to the economy and for Ireland's reputation.
Speaking on the same programme, he said both sides were going to have to move.
"This is a very serious situation. It is very damaging for our economy, for our reputation, for tourism and but more importantly, even than that, just the lives of ordinary people.
"We've listened to spokespersons from both the airline and the pilots saying that they're inviting each other to meetings and yet meetings aren't happening.
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So, there seems to be a disagreement even about the terms of engagement. And normally when two parties want to meet each other, it happens.
Mr McGrath said it was concerning that the Labour Court arrived at the view that there was not a foundation for further engagement at this time.
Sinn Féin TD Louise O'Reilly said industrial action has upended the holiday plans of thousands of families and workers.
She told the Dáil the consequences will be wide ranging with the tourism sector already experiencing falling bookings.
Given the seriousness of the dispute, there was a need for the Minister for Enterprise and Minister for Transport to intervene, she said.
Minister for Social Protection Heather Humphreys said the Government knows how frustrating the dispute is for people who have booked flights.
She said her heart goes out to parents and children who have been saving for months for their summer holidays.
The Labour Court remains available to both parties said Ms Humphreys and she urged them "to get back to the table" with "cool heads" and to leave "their egos at the door".
Additional reporting Mícheál Lehane
