On Monday, a loss of power at its headquarters in Atlanta led to the breakdown of the company’s booking and communications systems.
The airline was forced to cancel nearly 1,000 flights and delay close to 3,000 others worldwide.
Delta said it has addressed the issue but is still in “recovery mode”.
“We were able to bring our systems back on line and resume flights within a few hours yesterday but we are still operating in recovery mode,” said Dave Holtz, Delta’s senior vice president of operations and customer centre.
He said the company was doing everything it could to restore the system but warned more delays and cancellations were likely.
On Monday evening, Delta’s chief executive Ed Bastian, issued a video apology to passengers. The company has been offering refunds and $200 (£154) vouchers to passengers whose flights are cancelled or delayed by more than three hours.
The company has not said yet what the financial impact of the incident will be.
Delta is the third largest airline by passenger numbers in the world.
According to flight tracking service, FlightStats, over 600 flights had been delayed on Tuesday and 330 had been cancelled by mid-day.