Impact, the Irish pilots' union, said it had received Ryanair's letter on Friday morning.
The carrier said it would recognise these unions "as the representative body for pilots in Ryanair in each of these countries, as long as they establish committees of Ryanair pilots to deal with Ryanair issues, as Ryanair will not engage with pilots who fly for competitor airlines in Ireland or elsewhere".
Earlier Friday, Ryanair offered to recognise unions in a bid to halt a series of planned strikes by Europe-wide pilots working for the carrier ahead of New Year.
The Ireland pilots were to be joined in their action by Portugal, while pilots in Germany, Italy and Spain had all said that were considering undertaking industrial action.
Steve Cotton, general secretary of the ITF, said: "Ryanair must not stop at pilots' unions".
"We are ready to meet them today or tomorrow if necessary and we want to have that meeting just to make sure that there is substance to the offer they made in writing and to flesh out how that recognition process would proceed".
With his offer, Chief Executive Michael O'Leary is reversing a policy at the heart of the ultra low-priced model he developed to turn a small Irish regional airline into Europe's biggest by passenger numbers.
"Impact has indicated its availability to meet with Ryanair management today - or at any time over the coming weekend - to discuss these matters", the union said. It added it was considering the contents and would respond to the company before making a public statement.
"Ryanair has again called on IMPACT/ IALPA to cancel the threatened industrial action on Wednesday December 20 (as the Italian and German unions have already done) which is causing unnecessary concern and worry for thousands of Ryanair customers travelling home during Christmas week".
The company will "wait and see what comes" before deciding about recognising unions in other parts of the company, Chief People Officer Eddie Wilson told Reuters.
However, the airline had said it could not meet the unions before Wednesday.
Management will, though, be open to talking to pilots about their demand to introduce local contracts rather than the Irish contracts used across Ryanair's European bases.
Despite such difficulties, the airline thinks costs would increase as a result of unionization and last month said it still expected to deliver annual profit after tax of €1.4-1.45 billion ($1.65-1.71 billion).
Apart from the minimal design changes, the Star Wars Edition of the phone doesn't differ much from the original OnePlus 5T . But lighting it up will welcome you to a Star Wars wallpaper, which can be swapped with a series of Star Wars characters.
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It's meant to silence me", she said, adding , "It's not going to silence the women who stood up against him, directly. The Melrose Democrat added that Gillibrand's record of standing up for women "should really terrify" Trump.
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