Even after the US carrier lifted its initial flight grounding order about six hours after the computer snafu struck, it warned of continued cancellations and delays, as tens of thousands of passengers around the globe were left stranded.
Travelers crowded ticket counters, stretched out 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 resumed but on a limited basis, and Delta warned the ripple effect of the computer breakdown would drag on.
"While systems are improving and flights are resuming, delays and cancellations continue," the carrier said in a statement around midday.
Teams were working "around the clock" to bring systems back online, Delta CEO Ed Bastian said in a video message from the airline's operations center.
"As I'm sure you can appreciate, it's an all hands on deck effort," he said.
"I apologize for the challenges this has created for you with your travel experience."
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.
Very bad timing
At Los Angeles International Airport, people waiting for red-eye flights to the east coast dozed in a crowded waiting area, many of them wrapped in red blankets.
As of about 2300 GMT, the airline said it had cancelled more than 740 flights. Of 6,000 scheduled to have taken off by that time of day, it operated 3,340.
Delta has more than 15,000 flights a day along with its alliance partners.
"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).
Lines of passengers backed up at Delta ticket counters at US airports.
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, Delta offered refunds to travelers whose flights were cancelled or significantly delayed. People on some routes were being allowed to make a one-time change to their travel plans.
Delta announced Monday evening it was giving $200 travel vouchers in addition to refunding ticket values to customers who were delayed more than three hours or whose flight was cancelled.
A vast number of flight delays normally creates a cascading problem that affects airline traffic for days.
Computer outages halting flights are not uncommon.
In May, a glitch affecting Sweden's civil aviation authority radar site disrupted air traffic throughout that country and grounded flights to and from Stockholm for several hours.
In March, a computer system malfunction forced Japan's All Nippon Airways to cancel more than 100 domestic flights, affecting some 16,000 travellers.
And in mid-August 2015, a computer problem at a regional air traffic control center delayed hundreds of flights at busy US east coast airports -- including those in the Washington and New York areas -- for several hours.
A rival US airline, United, suffered computer glitches in May and July 2015 that temporarily grounded hundreds of flights and backed up thousands of passengers.