In September, British Airways said a computer problem in its check-in systems caused delays and long lines at numerous airports. "At this time, we are unable to process rebookings at airport terminals".
He also asked passengers not to arrive at Heathrow too early, warning they would not be admitted into Terminal 5 until 90 minutes before their flight's scheduled departure time.
"I know this has been a frightful time for customers", Cruz said.
"We are repositioning some aircraft during the night to enable us to operate as much of our schedule as possible throughout Sunday".
On Saturday, passengers at Heathrow and Gatwick faced long lines at check-in counters and the failure of both the airline's website and its mobile app. BA said the crash also affected its call centers.
BA is hoping to operate a near-normal service on Bank Holiday Monday, but is telling passengers who do not wish to risk disruption: "Even if your flight is still operating, you can get a full refund or rebook to travel up to the end of November".
BA has apologised over this incident which is believed to have been caused by a power supply issue and they have said passengers will be assisted in rebooking flights.
Thousands of British Airways customers could be eligible to claim compensation under an European Union law which gives consumers the right to compensation if their flight has been delayed by at least three hours or cancelled for reasons that are within control of the airline.
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The airline was hit by a worldwide computer system power failure on Saturday, causing cancellations and delays for thousands of passengers.
A spokeswoman for BA could not immediately detail the exact number of flights cancelled on Saturday. 'So we have no way of getting out of Heathrow and they haven't compensated us for anything, and we're stuck and this is the worst honeymoon ever.
"We did take some of their passengers on our flights out of our London gateways and I'm sure other airlines did as well and that's a regular industry practice to help affected passengers", an Emirates spokeswoman told The National.
Some passengers were curled up under blankets on the floor or sleeping slumped on luggage trolleys.
Gatwick and Heathrow told passengers not to travel to the airports unless they were rebooked on other flights.
"We helped her up and she said 'I'm just so exhausted, '" said Page, whose luggage didn't arrive in Texas with him.
Faced with long queues and uncertainty, some travellers made a decision to buy new tickets on other airlines.
While British Airways could face a one-off financial hit from the cancellations, the risk to its reputation among customers could be more damaging in the long-term effect.
BA has not said what is causing the computer problem, but says it has no evidence of a cyberattack.