BA said it aimed to operate the majority of services from London Heathrow on Sunday and a near normal schedule from Gatwick, the capital's second busiest airport. Heathrow authorities, however, said they expected further delays and cancellations of BA flights.
"We are continuing to work hard to restore all of our IT systems," BA added in a statement. "We are extremely sorry for the huge disruption caused to customers."
Heathrow told passengers not to travel to the airport unless they were rebooked on other flights.
British Airways cancelled all its flights from Heathrow, Europe's busiest airport, and Gatwick on Saturday after a power supply problem disrupted its flight operations worldwide and also hit its call centres and website.
A spokeswoman for BA could not immediately detail the exact number of flights cancelled on Saturday.
Alex Cruz, the chairman and chief executive of BA, part of Europe's largest airline group IAG, said there was no evidence of any cyber attack.
CHAOS FOR PASSENGERS
Thousands of passengers queued for hours in departure halls at the airports on a particularly busy weekend. Monday is a public holiday and many children were starting a one-week school holiday.
It is already facing declining customer ratings following unpopular decisions made as it faces competition from low-cost airlines. These include starting to charge for food on short haul flights last year to cut costs.
Terminals at Heathrow and Gatwick became jammed with angry passengers, with confused BA staff unable to help as they had no access to their computers, according to passengers interviewed by Reuters.
Some passengers expressed frustration on Twitter over missing bags and long waits in telephone queues to speak to BA staff.
"We are refunding or rebooking customers who suffered cancellations on to new services as quickly as possible," BA said, adding that it had introduced more flexible rebooking policies for passengers affected.
While other airlines have been hit by computer problems, the scale and length of BA's troubles were unusual.
Delta Air Lines Inc cancelled hundreds of flights and delayed many others last August after an outage hit its computer systems. Last month, Germany's Lufthansa and Air France suffered a global system outage which briefly prevented them from boarding passengers.
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