The low-cost airline's refusal to recognise unions was at the heart of the model that transformed the small Irish regional airline into Europe's largest carrier by passenger numbers.
Its shares were down as much as 5% in Friday trading.
Ryanair's offer came after the Irish Airline Pilots' Association (IALPA) had warned that its members working for the carrier were planning to walk out on Wednesday 20 December.
Such a move would involve half of the company's pilots - mostly captains - forcing Ryanair to cancel many services.
Ryanair said on Friday it had written to pilot unions in Ireland, the UK, Germany, Italy, Spain and Portugal in a bid to smooth turbulent industrial relations by offering talks on officially recognising the unions for the first time.