The Fórsa trade union has said the decision by Ryanair to threaten job losses in Dublin was not going to lead to pilots standing down their industrial action against the airline.
The airline said it plans to cut its Dublin-based fleet of aircraft from 30 to around 24.
However the company's chief marketing officer, Kenny Jacobs, said the decision to issue protective notice was a commercial decision and not made in response to recent strikes by pilots.
IALPA pilots at Ryanair have announced a fourth one-day strike for Friday 3 August in the dispute over base transfers, seniority and leave.
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Speaking on RTÉ's Morning Ireland, Bernard Harbour of Fórsa said an independent mediator could help the two sides to make progress.
On the same programme Mr Jacobs said that until the pilots union "come back to us" on Ryanair proposals then it is not time for third-party intervention.
Mr Jacobs said the airline is serious about working with unions and with Fórsa and wants all pilots and cabin crew to be happy.
He also claimed that an "unwanted" third party from outside the airline was interfering in the dispute.
Mr Jacobs said there is documented evidence that an individual from another airline was writing to the Dublin Airport Authority with details of the strike action subsequently announced by Ryanair pilots.
Mr Harbour rejected this claim, saying the people who go to the negotiations on their side are Ryanair pilots who represent their colleagues and full-time union officials who have no connection to any airline.
He said the talks to resolve this row have been delayed because of Ryanair.
Mr Harbour had said on Wednesday that the airline said they were not prepared to talk for at least another week.
"That will have been 20 days since we have sat down in a room when we get to the 4th of August. This is not going to be resolved unless there is negotiations."
He acknowledged the difficulties around that and again reiterated Fórsa's suggestion that third-party facilitation might assist both sides.
He said they are trying to achieve a simple thing, which is to have "agreement which governs transfers of pilots between bases".
