Ryanair staff have planned strike action on December 20.
On Saturday night, Ryanair offered to meet on Tuesday, but Impact refused to budge.
IMPACT says it wants to meet Ryanair sooner rather than later to see if Wednesday's planned strike action by pilots can be called off.
"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".
It said: 'The union has agreed to meet management on Tuesday evening, but says it is available to meet sooner.
The BALPA union said it had accepted Ryanair's offer to represent British-based pilots, but only if the TUC federation of British trade unions was allowed to attend future talks.
Mr Harbor said IMPACT had spoken to senior Ryanair management, telling them they were ready to meet them at any time.
Ryanair has agreed to recognize pilot unions ahead of a strike threat by a number of its pilots just ahead of the busy Christmas travel weekend.
RYANAIR will announce "contingency plans" for passengers facing a 24-hour strike in the run-up to Christmas tomorrow.
Chief executive Michael O'Leary admitted union recognition would be a "significant change" for the airline.
Ryanair has sought a meeting with the Irish Airline Pilots' Association on that day, according to The Independent.
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