He told the BBC the airline was struggling to process a backlog of 25 million refunds with reduced staff.
However, he pledged: “If you want a cash refund, you will receive a cash refund.”
Ryanair is set to cut 3,000 jobs – 15% of its workforce – as it restructures to cope with the coronavirus crisis.
It said the 3,000 posts under threat were mainly pilot and cabin crew jobs.
There are likely to be pay cuts of up to 20% for remaining staff, the airline added.
Mr O’Leary told the BBC that the planned cuts were “the minimum that we need just to survive the next 12 months”.
He said that if a vaccine was not found, “we may have to announce more cuts and deeper cuts in future”.
The restructuring could involve closing some UK regional hubs, Mr O’Leary said, but he would not say which ones were at risk.
He said Ryanair hoped to announce details of job losses and pay cuts by 1 July.
Mr O’Leary, whose pay was cut by 50% for April and May, has now agreed to extend it for the remainder of the financial year to March 2021.
Ryanair said it expected to report a net loss of more than €100m (£87m) for the first three months of the year, with further losses in the second quarter.
In a sideswipe at rivals, it said its return to scheduled services would be rendered more difficult by competing with flag carrier airlines, “who will be financing below cost selling with the benefit of over €30bn in unlawful state aid, in breach of both EU state aid and competition rules”.
Ryanair said it had entered the coronavirus crisis with reserves of almost €4bn in cash and continued to “actively manage” those resources in order to survive the pandemic.
Mr O’Leary described airlines such as Lufthansa, Air France and Alitalia as “subsidy junkies running around Europe hoovering up state aid”.
Meanwhile, Hungarian low-cost airline Wizz Air is resuming flights from Luton airport starting on Friday, but passengers will be required to wear masks while on board.
The airline is among the first European carriers to begin restoring services that have been suspended because of the coronavirus pandemic.
The flights will be heading for destinations in Spain, Portugal, Israel, Slovakia, Serbia, Romania and Hungary.
But Wizz Air warned that because of “rapid changes in travel restrictions, the list might be adapted”.
The move comes despite unchanged advice from the Foreign Office against all foreign non-essential travel.
In another development, London’s Heathrow airport, normally the busiest in Europe, has said it expects passenger numbers to have fallen 97% in April as demand slumped.
Numbers fell 18.8% to 14.6 million during the first three months of the year, the airport said.
But it added: “Heathrow remains open – and continues operating safely to help people get home and to secure vital supply lines for the UK.”
Financially, it was “robust”, it said.
“Heathrow has £3.2bn in liquidity, sufficient to maintain the business at least over the next 12 months, even with no passengers,” it added.
Heathrow chief executive John Holland-Kaye told the BBC’s Today programme that until a coronavirus vaccine could be developed, airports would have to introduce measures to minimise infection once lockdowns started to ease.
“What this might include – and this needs to be agreed with governments and the aviation sector – is a combination of measures and that might include some kind of health screening as you come into the terminal so that perhaps if that’s a temperature check, if you have a high temperature, you may not be allowed to fly,” he said.
“As you go through the airport, you will probably be wearing a face mask, as people from Asia have been doing ever since Sars came out.”
Coronavirus: Leaving middle seat empty is idiotic, says Ryanair
23 April 2020 (BBC)
The boss of Ryanair says the airline will not resume flights if it has to keep middle seats empty to fight Covid-19, calling the idea “idiotic”.
Michael O’Leary said he was hopeful 80% of flights could resume by October if travel restrictions are eased in July.
But he said empty seats did not ensure safe social distancing and were financially unviable.
He added that if the Irish government imposed the rule, it would have to pay for the middle seat “or we won’t fly”.
Like most other big airlines, Ryanair has grounded flights as countries around Europe have imposed travel restrictions to contain the pandemic.
However, industry experts believe the rules will relaxed this summer, subject to conditions.
Emirates, easyJet and Delta in the US have all said they plan to keep middle seats empty and some think governments will make it a rule.
But Mr O’Leary told the Financial Times the idea was “idiotic” as it did not ensure a safe 2 metre distance between passengers.
“We can’t make money on 66% load factors,” he said.
He said Europe should instead follow Asia and bring in more effective measures, such as forcing people to wear masks on transport and have their temperatures checked at airports.
Many in the airline industry believe it could take up to three years to get back on track.
According the UN’s civil aviation body, ICAO, international air passenger traffic in the first three quarters of 2020 could drop by as many as 1.2 billion travellers, or by two-thirds.
But Mr O’Leary told the Financial Times he was optimistic.
He said Ryanair expects a “relatively quick recovery”, with 80% of flights having resumed by September, falling to 60% in its less busy winter season.
He added that, subject to an effective coronavirus vaccine, the airline would be carrying its “2019 traffic plus growth” by summer next year.
However, he said it was likely the airline would have to cut jobs this winter and that he would continue to take a 50% pay cut beyond May if necessary.
“My pay cut will run on until the last of [Ryanair] people are off the payroll support schemes,” he said.
Meanwhile, the European Court of Justice ruled on Wednesday that Ryanair and other airlines must in future indicate the full price of a ticket when displaying offers online.
This means including the cost of value added tax on domestic flights and fees for check-in and payments by credit card.
The ruling came after an appeal by Ryanair against a decision by the Italian competition and markets authority, which said such charges were unavoidable and foreseeable, and should therefore be included in the price shown before booking
The BBC has approached the airline for comment.