Delta Air Lines canceled more than 600 flights on Monday, hours after Secretary of Transportation Pete Buttigieg singled out the airline as it struggles to recover three days after a global software outage grounded flights around the world.

Mr. Buttigieg said on Sunday that his office had received complaints about Delta’s customer service, and warned that the carrier must provide its customers with adequate assistance and refunds. Delta canceled about 1,300 flights on Sunday, roughly the same number as each of the previous two days, and delayed another 1,600, according to flight tracking website FlightAware. The cancellations represented about a third of its scheduled flights.

Delta’s cancellations on Monday — 607 as of 7 a.m. ET — accounted for about 16 percent of its scheduled departures.

The tech outage on Friday hit airlines especially hard. A flawed update from CrowdStrike, whose software is used around the world, forced Allegiant Air, American Airlines, Spirit Airlines and United Airlines to ground flights, according to the Federal Aviation Administration.

Delta has been the slowest to restore its operations. It canceled about 1,200 flights each on Friday and Saturday, according to FlightAware, while cancellations for other airlines moderated into the hundreds or dozens.

In a statement on Sunday, Delta’s chief executive, Ed Bastian, apologized to customers. “Canceling a flight is always our last resort, and something we don’t take lightly,” he said.

The outage, which disrupted devices that run Microsoft Windows software, had affected one of Delta’s crew tracking-related tools, Mr. Bastian said.

Delta had offered travel waivers to all customers booked on flights between Friday and Sunday, allowing them to change their flights once for free, the statement said, and was offering meal vouchers, hotel accommodation and transportation where available.

Mr. Buttigieg said in a social media post on Sunday night that the Department of Transportation had received hundreds of complaints about the airline. Delta must provide prompt refunds to customers who do not want rebooked flights, and timely reimbursements for food and hotel stays for those affected by the delays, he said.

“No one should be stranded at an airport overnight or stuck on hold for hours waiting to talk to a customer service agent,” Mr. Buttigieg said, adding that customers should report airlines that fail to honor their customer service requirements to the agency.

Airlines initially treated the outage as something that was inherently outside their control, for which their only obligation to passengers was free rebookings. However, the Transportation Department said on Friday that software outage was considered within airlines’ control, and U.S.-based airlines must provide affected customers compensation for flight disruptions.