On Saturday night, Ryanair offered to meet on Tuesday, but Impact refused to budge.
It has asked the airline to release its pilot representatives so they can prepare for and attend the meeting.
"Putting the needs of our customers first, and avoiding disruption to their Christmas flights, is the reason why we will now deal with our pilots through recognised national union structures and we hope and expect that these structures can and will be agreed with our pilots early in the New Year".
Unions representing Ryanair pilots in Ireland and Portugal on Sunday suspended plans to strike before Christmas, lifting the threat of industrial action at the low-priced giant after it agreed on Friday to recognise trade unions for the first time.
It said it would "not engage with pilots who fly for competitor airlines in Ireland or elsewhere".
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The suspended industrial action had been planned with the support of 94 percent of pilots directly employed by Ryanair in Ireland.
Ryanair said on Friday it would recognise unions but IMPACT says further clarifications are needed.
Friday's announcement led to Italian pilots' union Anpac and Portuguese union Spac calling off strike action due to take place next week.
It will bring certainty to Ryanair passengers travel plans over the Christmas period.
In Spain, there are no strikes planned for pilots but ground staff unions have not ruled out action on 30 December.
Ryanair has sought a meeting with the Irish Airline Pilots' Association on that day, according to The Independent.