"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 next week", said Mr O'Leary this morning.
Ryanair has said it will recognise pilot unions for the first time, in an effort to avert its first pilot strike threatened for later on Friday.
It said its pilots had chose to strike because Ryanair was refusing to offer contracts under local rather than Irish law and to recognise the union's company council as its exclusive negotiating partner in Portugal.
A spokesman for Ireland's Impact Union, which includes the pilots' association, said Friday it would respond to Ryanair after studying the proposal.
The airline was also facing action by pilots in Italy, Germany and Portugal.
Ryanair refuses to recognise unions, insisting instead on its own system of collective bargaining.
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Ryanair has never recognised unions, but it said it would change this policy in order to avoid disruption to flights and passengers in Christmas week.
One day of industrial action had been planned for Wednesday December 20 and would have mostly involved captains.
Around 30% of the airline's Irish-based pilots are set to take part in the strike just five days before Christmas.
A German pilot union was also understood to be preparing to announce a strike by Ryanair pilots next week.
The low-priced carrier sent the offer to representative bodies in the UK, Ireland, Germany, Spain, Italy and Portugal - the only time Michael O'Leary has sought such a deal in the 32 years of the airline.
The airline said it would recognise the unions as long as the pilots were willing to establish Committees of Ryanair pilots to deal with Ryanair issues, as the airline said it would not engage with pilots who fly for competitor airlines in Ireland or elsewhere.