Ryanair sent a letter to unions in Ireland, Britain, Germany, Italy, Spain and Portugal at 0800 GMT on Friday to offer talks to formalise recognition and asking for confirmation that industrial action would not proceed.
Ryanair offered on Friday to recognise pilot unions for the first time in its 32-year history in a last-minute attempt to avert its first-ever pilot strike.
It had been expected that the number of Ryanair employees involved in next Wednesday's planned strike would be fewer than the total number of Irish-based Ryanair pilots.
"Ryanair has also offered to meet IMPACT/IALPA and their Ryanair pilot committee on Tuesday 19 December if that would suit them better", added the statement.
Steve Cotton, general secretary of the ITF, said: "Ryanair must not stop at pilots' unions".
A one-day strike had been planned for Wednesday December 20 and would have mostly involved captains operating out of Irish bases but doubtless have a severe knock-on effect.
This was great news for many, but the pilots union, IMPACT still intend to strike if the airline can not meet before the strike date.
However, the airline had said that management would not be able to meet with IMPACT representatives until Wednesday.
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The European Transport Workers' Federation (ETF) and International Transport Workers' Federation (ITF), which represent pilots and cabin crew in all of Europe's major airlines, also wrote to Mr O'Leary to say they are open to talks on union recognition.
Trade unions are willing to open talks with Ryanair after the low-priced carrier made a dramatic U-turn and offered to recognise pilots' unions for the first time in its history.
"Given the seriousness of the situation I think it would be good if they could move their diaries around and find availability", he said.
No details have been provided by the airline of how many, or which, flights are likely to be affected.
Her organisation has affiliates in about 150 countries, including Siptu and Impact in the Republic.
Ms Blackshaw said unions wanted to tackle issues such as direct employment and discuss pay, rosters and other conditions.
The pilots mobilised after Ryanair in September announced the cancellation of around 20,000 flights, which it blamed on a lack of standby pilots due to a failure in its rostering following a rule change by Irish regulators.
At this point, it seems that all eyes are on Ryanair to prevent this strike. "They've gotten our offer of recognition in writing and we're happy to meet them next week, which itself is the first act in recognising IALPA", Ryanair said.