The company said large-scale cancellations are expected today but that all flights already en route are operating normally. Delta has published a waiver for customers traveling on 8 August through to 12 August.
"We are aware that flight status systems, including airport screens, are incorrectly showing flights on time. We apologize to customers who are affected by this issue, and our teams are working to resolve the problem as quickly as possible," Delta said.
The airline said passengers should check the status of their flights this morning while the issue is being addressed.
"Delta has experienced a computer outage that has affected flights scheduled for this morning. Flights awaiting departure are currently delayed. Flights enroute are operating normally," the company said earlier.
The company, the second biggest airline in the US, has been fielding questions from passengers on social media.
"I am really sorry for the inconvenience. Our systems are down everywhere. Hopefully it won't be much longer," Delta said on its Twitter account.
"Unfortunately all flights are grounded due to a system outage nationwide," it added.
@Jessb6484 Hi there. I am really sorry for the inconvenience. Our systems are down everywhere. Hopefully it won't be much longer. *SD
On Twitter the company said its IT team was "working on some network issues that are impacting several applications, including our website".
The airline has more than 80,000 staff and 800 aircraft, and transports more than 180 million passengers a year to 335 destinations. Its largest hub is Atlanta -- where it is headquartered -- with more than 1,000 daily departures to 223 destinations.
UPDATE at 8.40AM eastern time (12.40 PM GMT) Delta said limited departures are resuming following the power outage, although cancellations and delays continue.
It warned: "Customers heading to the airport should expect delays and cancellations. While inquiries are high and wait times are long, our customer service agents are doing everything they can to assist. There may also be some lag time in the display of accurate flight status at delta.com, the Fly Delta App and from Delta representatives on the phone and in airport."