Irish based Ryanair pilots have just announced they will hold another one day strike in August, on Friday the 10.
Forsa said in a statement: "Ryanair's announcement that it will accept independent third-party assistance in its dispute with pilots, which was made without preconditions, is an unexpected and positive development".
On Thursday, pilots warned there would be a fifth day of strikes on August 10, when the airline's Belgian and Swedish pilots will also be on strike.
It said that the pilots continue to seek a "fair and transparent method" to govern base transfers and related matters which they say is common practice in the industry.
The Forsa trade union, which had called for such a move, welcomed Ryanair's response and said it would recommend to pilots.More news: Corbyn tells Labour anti-Semites `you have no place in our movement´
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"Even when Ryanair invites FORSA to more meetings, FORSA just calls more strikes".
This is the fifth strike by pilots since July 12. "FORSA should now explain why another 3,500 Irish customers will have their flights and holidays next Friday 10 Aug disrupted when FORSA have refused not one, but two invitations to meet with Ryanair to resolve this dispute". "The union has today told Ryanair that it remains available for talks".
"The airline's escalation of the dispute last Wednesday when it threatened to sack 100 pilots and 200 cabin crew, or transfer them to Poland - led to a predictable hardening of resolve among its staff".
"We now call on Forsa to accept Mr Mulvey as a third party mediator, an initiative Forsa have repeatedly called for in recent weeks", he said.
Ryanair is seeking to make separate agreements in each of the markets it operates and has asked for a full week's notice of strike action to refund or redirect passengers.