He called on Ryanair to respond swiftly to the request for a signed document as the union does not want "to be in an industrial action phase".
The airline was due to meet German and Portuguese pilot unions this week, as well as representatives of Ialpa, a branch of the Impact union in Ireland.
"While Ryanair management said they recognized IMPACT/IALPA for collective bargaining purposes at this evening's meeting, they said they were unable to give the union a piece of paper to confirm this", the union said.
Ryanair Holdings Plc's Irish pilots gave the company less than two days to come up with a agreement to recognize their labor union.
The first-ever talks between unions and management at Ryanair will take place later.
The conditions at the training centre apply to thousands of cabin crew hired by third-party agencies for Ryanair
Ryanair's announcement that it will also recognise cabin crew unions comes after renewed focus on its treatment of lower-paid staff.
Financial analysts had calculated yesterday that the decision to recognise pilots unions could add €150 million to the annual payroll - with an even higher cost once unions representing 8,000 cabin crew are factored in.
Mr O'Leary said the move was "putting the needs of our customers first, and avoiding disruption to their Christmas flights".
It was the first meeting between the airline and a trade union in the company's 32-year history.
According to a recording of a meeting obtained by the Irish Independent newspaper, Ryanair executives told pilots at Stansted last week that the airline had "grown too fast" and lost their trust, but was working hard to restore it.
"Recognising unions will be a significant change for Ryanair, but we have delivered radical change before", Michael O'Leary said. "We're decisive in it", he said.