Even after the US carrier lifted the order about six hours into the snafu, it warned of continued cancellations and delays, as tens of thousands of passengers around the globe were left stranded.
Travelers crowded ticket counters, lay on the ground in airports and tried to grin and bear it. Ticket agents were reduced to checking people in manually, news reports said.
The carrier blamed the computer problem on a power outage in its hub in Atlanta, Georgia.Flights have resumed but on a limited basis, Delta said in a statement after flights had been grounded for about six hours. However, the ripple effect of the meltdown will drag on.
"While inquiries are high and wait times are long, our customer service agents are doing everything they can to assist," it added.
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It also said there would 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."
Luciano Resende, 40, waiting at London's Heathrow Airport to fly to San Francisco, said it was slow going.
"I guess it has been a long time since they used the manual process," Resende told NBC News.
As of about 1400 GMT, the airline said it had cancelled about 300 flights. It operates more than 15,000 a day along with its alliance partners.
Nearly 400 others were delayed, according to flight-tracking service FlightAware.
"The timing of this problem is particularly bad because Monday morning is one of the busiest times for both airlines and travelers as business travelers begin their work week," said Daniel Baker, FlightAware's CEO.
Delta said the power outage in Atlanta that caused the computer meltdown began at 2:30 AM (0630 GMT).
At Los Angeles, passengers on a flight to New York had to get off their plane and return to the terminal, NBC News reported, while some people slept near departure gates at Las Vegas.
As compensation for the inconvenience, Delta offered refunds to travelers whose flights are cancelled or significantly delayed. People on some routes are being allowed to make a one-time change to their travel plans.