The firm's boss Alex Cruz has promised compensation to customers affected by the "criminal attack" on the airline's website, which compromised personal and financial details of people making bookings.
Speaking to the BBC's Today programme, he said: "We are 100% committed to compensate them, period.
"We are committed to working with any customer who may have been financially affected by this attack, and we will compensate them for any financial hardship that they may have suffered."
Around 380,000 transactions were affect, but it's been clarified that the stolen data didn't include passport or travel details.
The breach took place between 22.58 BST on August 21 and 21.45 BST on Wednesday (05.09.18).
Mr. Cruz has acknowledged the "concern" caused to customers, and explained the process of informing them about the incident.
He added: "We're extremely sorry. I know that it is causing concern to some of our customers, particularly those customers that made transactions over BA.com and app.
"We discovered that something had happened but we didn't know what it was [on Wednesday evening]. So overnight, teams were trying to figure out the extent of the attack.
"The first thing was to find out if it was something serious and who it affected or not. The moment that actual customer data had been compromised, that's when we began immediate communication to our customers."