Around 4,000 Ryanair customers face the disruption of cancelled flights during a second pilots strike on Friday.
The airline has cancelled 24 flights to the UK, including from Dublin to Glasgow, Newcastle and Manchester, during the 24-hour stoppage.
Another 4,000 customers face disruption next Tuesday if a third strike goes ahead.
A senior official at the airline said he has high hopes the Irish Airline Pilots Association division of the Forsa union will call off next week's stoppage.
Chief marketing officer Kenny Jacobs was speaking as both sides are expected to meet to discuss the pilots' demands for better terms and conditions.
If next week's strike goes ahead, almost 13,000 passengers will have suffered disruption since the industrial action began. It has been revealed that some passengers were reaccommodated on Aer Lingus flights to reach their destinations.
Ryanair cancelled flights on high frequency routes yesterday and all customers affected received text and email notifications. Customer service teams are organising refunds and transfers to alternative flights.
"We apologise again to these Irish customers for these regrettable and unnecessary disruptions, which we have done our utmost to avoid," said the airline in a notice to customers.
Pilots want the roll-out of a 'seniority list' to determine who gets holidays, base transfers and promotions. However, the airline claims such a system would put it at a disadvantage.
Mr Jacobs said no family holidays to the sunshine have been disrupted so far and won't be by Friday's strike.
"Hopefully Tuesday's strike will be called off," he said.
"We're working to bridge the gap in understanding between the proposals we've made and what they want. They don't understand some of the things we're explaining."
He said if a seniority system was in place, a captain based in Berlin who was up the list because they had longer service, could displace an Irish captain if their base was downsized.
Mr Jacobs said you could not "copy and paste" a model that worked at Aer Lingus into Ryanair's business model.
Ryanair said just a quarter of around 350 of their pilots voted to strike on Friday.