Among those cancellations announced for the next three days include dozens of flights to and from Spanish destinations.
Monday saw the cancellation of 19 flights either to or from Spanish airports, while 16 Spanish flights on both Tuesday and Wednesday were grounded.
Of the more than 140 flights cancelled at the weekend, almost 40 flights were to or from Spanish airports.
For passengers whose flights are cancelled and who opt to fly later, European passengers' rights are clear. Ryanair is legally obliged to provide meals and accommodation as appropriate, together with cash compensation of €250 or €400 for journeys of 1,000 miles or more.
Ryanair could face up to 20m euros (£18m) in compensation claims from those whose flights were affected.
Ryanair's marketing director, Kenny Jacobs, said: “Cancellation notices for flights cancelled up to and including Wednesday 20th September have been sent to affected customers and posted on the Ryanair.com website.
“We will continue to send regular updates and post flight information on our website, with the next set of cancellations to be issued on Monday. We apologise sincerely to all affected customers for these cancellations.”
But Ryanair is under pressure to publish a full list of the flights it plans to cancel every day amid growing anger among customers.
UK consumer rights group Which? said: "It's essential that Ryanair release a full list of flights that will be affected so that passengers have as much time as possible to make alternate arrangements."
The airline has blamed a backlog of staff leave for the disruption, which could affect up to 400,000 passengers.
Ryanair is changing its holiday year, which currently runs from April to March, to run from January to December instead.
This has led to large numbers of its staff taking holidays in September and October.