Management's move was "a very important first step," the Associazione Nazionale Professionale Aviazione Civile (Anpac) said in a statement, calling on its members to "suspend the strike scheduled today at 1-5 pm" local time.
Earlier, Ryanair chief executive Michael O'Leary had announced a conditional offer to recognize pilot unions in Britain, Germany, Italy, Spain and Portugal, saying that "Christmas flights are very important to our customers and we wish to remove any worry or concern that they may be disrupted by pilot industrial action."
The Dublin-based airline said it would recognize the unions "as long as they establish committees of Ryanair pilots... as Ryanair will not engage with pilots who fly for competitor airlines".
Ryanair pilots based in Ireland and Portugal have strikes planned for Wednesday. Germany-based pilots have agreed to unspecified strike action.