The data could include personal information and payment card details and as a result, the airline is urging customers to check with their banks.
He said the attackers had not broken the airline's encryption but did not explain exactly how they had obtained the customer information.
"The breach has been resolved and our website is working normally".
"We take the protection of your personal information very seriously".
BA said it was investigating the vast breach "as a matter of urgency", while the National Crime Agency and National Cyber Security Centre are also assessing the hack.
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He said the company was "100% committed to compensate" customers. We have notified the police and relevant authorities. "There were other methods, very sophisticated efforts, by criminals in obtaining the data", he said. "We will be contacting customers and will manage any claims on an individual basis". "We discovered that something had happened, and immediately we began to work", he said.
"I´ve not heard anything from them on this and I´ve just had to cancel the card I used".
The head of British Airways Alex Cruz expressed regret for the incident and apologized to customers.
Customers due to travel can check in online as normal. It is now vital that the company moves quickly to ensure those affected get clear information about what has happened and what steps they should take to protect themselves.
Some 75,000 passengers were left stranded after a glitch forced the airline to cancel almost 726 flights over three days.
Consumer advice website MoneySavingExpert says customers should monitor bank and credit card statements closely for signs of possible fraudulent activity.