Ryanair management has invited the pilots' union Fórsa to meet for talks next Tuesday at Dublin Airport's Terminal 1 building.
In a letter to Fórsa National Secretary Angela Kirk, Chief People Officer Eddie Wilson proposes the meeting "...as long as no further strike is called prior to meeting (to allow this meeting to occur)".
He acknowledges that a pilot strike scheduled for this Friday will proceed and that 20 flights have already been cancelled, with 3,500 passengers disrupted.
He says it is irresponsible of Fórsa to call a fourth strike day by a quarter of the pilots because they are not happy with the wording of Ryanair's agreement to elements of the pilots' demands.
Ryanair and Fórsa have disputed the level of common ground between them.
The union's response to the Ryanair invitation is awaited.
Ryanair's Irish-based directly employed pilots were the first to strike in the dispute over conditions.
Pilots at the airline based in Belgium and Sweden have announced that they will strike on Friday week, 10 August, as the industrial dispute at Europe's largest airline escalates.
The German pilots union, VC has also backed strike action.
It has given the airline until next Monday to come up with "workable proposals", and will hold a press conference on Wednesday to announce its next move.
In addition, yesterday, Ryanair's pilots based in the Netherlands voted almost unanimously to join the campaign of industrial action - but have as yet given no indication of a strike date.
The unrest has also spread to cabin crew, who went on strike in Spain, Portugal, Italy and Belgium for two days last week, forcing the cancellation of 600 flights with disruption for 100,000 passengers.
A number of pilot sources say staff are angered by Ryanair's issuing of protective notice to 300 Irish-based pilots and cabin crew, along with a threat to move planes out of Dublin this winter, with potential consequential job losses for staff.
The Irish-based pilots union, Fórsa, has told the airline that this Friday's strike will proceed and that, if the dispute is not resolved, further strike dates will be announced "in due course".
The warning comes in a response from Fórsa National Secretary Angela Kirk to Ryanair's latest invitation to talks.
She told Mr Wilson that, subject to rostered duties, IALPA/Fórsa representatives remain available to meet the company to resolve all the matters between them, but at a neutral venue.
However, she warned the airline that its decision to serve notice of collective redundancy and other measures including involuntary transfer to Poland only serves to escalate the dispute and take the two sides further from reaching an agreed solution.
Ms Kirk rejected Ryanair's claim that it has agreed nine of the eleven pilot demands on a seniority agreement to govern the allocation of transfers leave and promotions, adding that failure to agree their eleven "minimum" requirements would see the union side announcing further strikes.
She also said that "...the re-wording and consequently the misrepresentation of our position in your briefing document is not conducive to a constructive engagement".
Speaking in Austria just yesterday, Ryanair Chief Executive Michael O'Leary reiterated that threat.
Belgian union official Didier Lebbe said the events since the pilot shortage last September to this summer's strikes clearly showed the limitations of the Ryanair model of which Mr. O'Leary was so proud.
He called for the withdrawal of the protective notice issued to Irish staff, and urged Belgian pilots to support their Irish colleagues and join the strike action which will take place in 10th August in several European countries.
The pilots' demands include the application of local law rather than Irish law to their employment contracts and a seniority based system for the allocation of base transfers, annual leave and promotions.
They also object to Ryanair's restrictions on who may form part of the union delegations at negotiations.
In a statement, the airline said that it "has received notice of strikes on Friday 10 August next by pilot unions in Belgium and Sweden.
"We have also been notified of possible strike actions by pilot unions in Germany and the Netherlands which we believe will be coordinated and occur on Friday 10 August.
"We have written to each of these pilot unions today and invited them to meet us in the coming days to make further progress in concluding union recognition and collective labour agreements in each of these markets.
"In the interim, we have requested these pilot unions to give us seven days' notice of any planned strike action so that we can notify our customers of cancelled flights in advance and offer them alternative flights or refunds."