The airline’s check-in systems and passenger advisory screens were affected during a systems failure early on Monday (August 8) at a number of terminals.
Delta’s website and smartphone apps were also affected by the issues, which as a result led to thousands of travellers struck by delays in the UK, Japan, Italy and US.
By Monday evening, the airline said it had cancelled more than 740 flights although its computer systems were working again.
Due to the problems, Delta has offered refunds and $200 (£153) travel vouchers for passengers who suffered delays of more than three hours or had their services cancelled, while chief executive Ed Bastian apologised to travellers in a video message.
“I apologise for the challenges this has created for you with your travel experience,” he said. “The Delta team is working very, very hard to restore and get these systems back as quickly as possible.”
“I appreciate the hard work the Delta team and the Delta people are doing to bring our system back up as quickly and safely as possible. And once again I apologise for any inconvenience this has caused to you our customer.”
Chief operating officer Gil West said: “We know that travellers value our commitment to excellent operational performance, and today we did not deliver on that commitment.
“We want our customers to know we are thoroughly investigating the matter and that we are truly sorry.”