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.
Impact, which represents Irish-based pilots, has agreed to meet the low-priced carrier's management on Tuesday evening ahead of the planned strike on Wednesday.
The British and Italian pilots' unions have agreed to meet in early January.
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.More news: Canadian billionaire and wife found dead in 'suspicious' circumstances in Toronto home
It will bring certainty to Ryanair passengers travel plans over the Christmas period.
"If the best way to achieve this is to talk to our pilots through a recognised union process, then we are prepared to do so, and we have written today to these unions inviting them to talks to recognise them and calling on them to cancel the threatened industrial action planned for Christmas week".
Impact, the Irish pilots' union, said it had received Ryanair's letter on Friday morning.More news: Alert : New York blast was 'attempted terrorist : mayor
Ryanair said on Saturday that it would meet the German pilots' union for talks on Wednesday.
In Spain, there are no strikes planned for pilots, but ground staff unions have not ruled out action on December 30.
Chief executive Michael O'Leary admitted union recognition would be a "significant change" for the airline.
The threat of a wave of strike action across Europe by Ryanair pilots prompted the airline to make one of the biggest U-turns in its history on Friday.More news: U.S. envoy says real dialogue needed with North Korea