While the decision to recognise trade unions for the first time in Ryanair's 32-year history has averted the threat of strikes, the move rattled investors and its shares fell nearly 9 percent on Friday.
Niall Shanahan, a spokesman for Impact, a union to which IALPA is affiliated, said: "We indicated to Ryanair that we were happy to meet them on Wednesday, but we would not be in a position to consider suspending the scheduled industrial action until we met them".
Impact, the Irish pilots' union, said it had received Ryanair's letter on Friday morning.
Ryanair staff have planned strike action on December 20.
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Impact initially responded today by saying it would not suspend the walk-out until after meeting Ryanair, but announced in a statement this evening that the strike was off.
It has asked the airline to release its pilot representatives so they can prepare for and attend the meeting.
O'Leary noted that the move would mark a significant change for the airline.
While some unions agreed to suspend action, the Irish Air Line Pilots' Association wanted more clarification.
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It is the only time airline boss Michael O'Leary has extended such an invite to union leaders in the 32 years the company has been in business.
Ryanair, Europe's second-largest airline by passenger numbers, has been forced to cancel 20,000 flights through to March because of pilot scheduling problems stretching back to September.
"Christmas flights are very important to our customers and we wish to remove any worry or concern that they may be disrupted by pilot industrial action next week", he said.
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