Up to 117 members of the Irish Airline Pilots' Association still plan to strike on Wednesday.
The statement added: "The union acknowledged the principled determination of Ryanair pilots which it said had made this breakthrough possible and said it looked forward to establishing a positive relationship with Ryanair company management".
Union spokesman Niall Shanahan has welcomed the progress, but said that they can not call off the strike just yet.
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Union chiefs had earlier insisted the strike action would go ahead unless management agreed to meet before Wednesday.
Mr Harbor said IMPACT had spoken to senior Ryanair management, telling them they were ready to meet them at any time.
But, in a statement released on Sunday evening, the union said it is available to meet sooner.
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However, a majority of pilots used by the airline in Ireland are not directly employed by the company.
He said that talks with pilots' unions would start next week, or in January at the latest, in all of Ryanair's European hubs, but he also said the company was not prepared to extend talks to flight assistants, who also demand union recognition. "If the best way to achieve this is to talk to our pilots through a recognized union process, then we are prepared to do so, and we have written today to these unions inviting them to talks to recognize them and calling on them to cancel the threatened industrial action planned for Christmas week".
In Spain, there are no strikes planned for pilots, but ground staff unions have not ruled out action on December 30.
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Bellew, whose predecessor resigned in October amid flight cancellations chaos forced by pilot shortages, said the budget airline opted for "dialogue" because it did not "want to put at risk [its] customers' Christmas".