Ryanair's chief people officer, Eddie Wilson, said: "Given the non-engagement by Forsa, and the manipulation of the discussions by certain Aer Lingus pilots to ensure that no meetings take place, that unsuccessful strikes keep repeating, Ryanair now feels the only way to introduce common sense is by way of third party mediation, and is suggesting Mr Kieran Mulvey, formerly of the Labour Commission and Workplace Relations Commission".
Disagreements between the union and Ryanair over promotions and seniority have continued.
More strikes are on the way as pilots in Ireland, Belgium and Sweden plan a walk-out, while German and Dutch cabin crew have also voted for a work stoppage.
Ryanair cancelled around 20 of Friday's 300 Irish flights as a result, mainly on busy routes to and from Ireland and Britain, and has said impacted passengers have either been put on another flight or refunded.More news: Portugal breaks temperature records amid heatwave
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The airline is bracing itself for another round of strike action next Friday, when 25 per cent of its pilots will strike. The Irish cancellations alone will affect around 3,500 passengers.
Ryanair has said it will shift jobs and planes to more profitable areas, and threatened to move more if the strikes continue.
The notice came just one day after Ryanair offered a meeting with Forsa on next Tuesday morning under the conditions that no more strikes will be called by the union before the proposed meeting.
But staff counter that this creates huge insecurity for them, blocking their access to state benefits in their country and stopping them from applying for mortgages. The airline had also until recently refused to recognize unions, but is gradually doing so as pressure increases.
A Ryanair Boeing 737-800 airplane takes off from the airport in Palma de Mallorca, Spain, July 29, 2018.
Ryanair did not respond to a request for immediate comment.