Delta Air Lines is struggling to restore normal operations after last week's crippling global cyber outage, cancelling over 5,000 flights since Friday.

Delta on Sunday cancelled 1,250 flights beyond the 3,500 it had already scrapped after a software update by global cybersecurity firm Crowdstrike triggered system problems for Microsoft customers, including many airlines, on Friday.

Delta has offered no timetable for resumption of normal operations and has already cancelled another 305 flights for Monday, according to the flight tracking website FlightAware.

Delta has operations in five Canadian airports, with cancellations of a few departures and arrivals from New York City and Atlanta already logged for Monday at the main airports in Toronto and Montreal. Select Delta flights from Detroit to Montreal, and to and from Minneapolis out of Vancouver, were also scrapped.

WATCH l Still many unanswered technical questions after Crowdstrike outage:

How the CrowdStrike-Microsoft global tech outage unfolded

The National explains how a CrowdStrike software update crashed Microsoft Windows, triggering a tech outage that disrupted industries around the world. Ian Hanomansing asks cybersecurity expert Ritesh Kotek to break down how a similar outage could be prevented.

The issue has stranded thousands of Delta travellers across the United States, with some having to rent cars to drive hundreds of miles while others could have to wait days for new flights or cancel trips altogether.

The Atlanta-based airline's Sunday cancellations represented one-third of its schedule, with 44 per cent of flights — about 1,7000 — delayed. 

For comparison, United Airlines cancelled about nine per cent, or 266, of Sunday flights, the second-most among carriers.

Hundreds of complaints to U.S. agencies

Delta CEO Ed Bastian said the issue affected its Microsoft Windows systems, snarling a critical application.

"In particular one of our crew tracking-related tools was affected and unable to effectively process the unprecedented number of changes triggered by the system shutdown," Bastian told customers in an email.

In a separate note, he told employees that Delta would continue to "tactically adjust" schedules to ensure safety.

Delta's website advises customers of the ongoing recovery from the tech issue, pointing them to a page on delayed and cancelled flights for rebooking and refund options.

Transportation Secretary Pete Buttigieg is calling on Delta to ensure passengers are treated appropriately after his department received what he said were hundreds of complaints.

"Delta must provide prompt refunds to consumers who choose not to take rebooking, free rebooking for those who do, and timely reimbursements for food and hotel stays to consumers affected by these delays and cancellations, as well as adequate customer service assistance," said Buttigieg.

"No one should be stranded at an airport overnight or stuck on hold for hours waiting to talk to an customer service agent."

Crowdstrike has said a significant number of the 8.5 million affected Microsoft devices were back online.