Alex Cruz told the BBC that hackers carried out a “sophisticated, malicious criminal attack” on its website.
The airline said personal and financial details of customers making or changing bookings had been compromised.
About 380,000 transactions were affected, but the stolen data did not include travel or passport details.
“We are 100% committed to compensate them, period,” Mr Cruz told the BBC’s Today programme. “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.”