“I can’t imagine that it doesn’t boost the focus in certain areas, maybe shift priorities based on what we learned,” Chief Executive

Bob Jordan

told reporters Thursday. “This has been an incredible disruption, and we can’t have this again.”

Southwest canceled nearly two-thirds of its flights Tuesday, Wednesday and Thursday, as part of an effort to dig out from a cascading meltdown after last week’s severe winter storm threw operations into disarray. While other airlines were able to recover from the brutal weather within a few days, Southwest continued to spiral.

Southwest has canceled nearly 16,000 flights in the past week, according to FlightAware. The airline scrubbed 39 flights scheduled for Friday that Chief Operating Officer

Andrew Watterson

said it was unable to staff, but executives said they believe they are ready for a smooth operation Friday.

Mr. Jordan told employees Thursday morning in a video message that shrinking Southwest’s operations had helped, with 95% of its flights on time on Wednesday. “Together we did what we needed to do to set ourselves up to operate our regular schedule tomorrow,” he said.

As it works to resume normal operations, Southwest faces heightened scrutiny from regulators and lawmakers, who have said they are closely monitoring the airline’s response to the crisis.

Transportation Secretary Pete Buttigieg on Thursday wrote to Mr. Jordan, describing the disruption as “unacceptable.” He reiterated his expectation that the airline will assist stranded passengers, honor commitments to cover passengers’ expenses, issue prompt refunds and ensure passengers are reunited with their bags. The airline has said it is providing those accommodations now.

Union leaders who represent Southwest pilots, flight attendants and other workers have faulted what they said was the airline’s lack of investment in technology over the years for many of its problems. Executives have acknowledged the need to upgrade inadequate platforms, such as the SkySolver system that it uses to redo crew schedules during disruptions and that was overwhelmed by the magnitude of the problems over the weekend.

Baggage Stuck in Southwest Airlines Cancellation Fiasco

Mr. Watterson said Thursday in a call with reporters that the upgrading process had already been under way. Southwest has made crew-scheduling its own department, hired more staff and made what he described as incremental improvements to current systems as it began to look for replacements. He said the “modest work” that had been done had started to pay off this fall, but that the winter storm created unique challenges.

While the airline has started to contemplate the broader questions of what it could have done differently, executives said their more immediate task this week has been to piece the airline back together—making sure that pilots and flight attendants are where they need to be, reuniting bags with their owners and ensuring that planes are tuned up and ready to go.

In an effort to make sure the airline is ready for Friday, Southwest added some flights for passengers on Thursday and ferried planes and crew to position them, Mr. Watterson said.

Ticket sales resumed, executives said, after the airline had limited bookings on remaining flights for much of this week, hoping to avoid a scenario where customers bought seats on flights that would ultimately be canceled. The airline also wanted to make sure seats would be available to take pilots and flight attendants where they had to be on Friday, Mr. Watterson said.

To get to this point, Southwest sought volunteers to help work through a deluge of tasks to repair schedules for pilots and flight attendants.

At the height of the disruption, the airline’s crew schedulers had to revert to manually assigning pilots and flight attendants to flights when automated software couldn’t keep pace with the volume of changes. Even with the smaller schedule, the group was overwhelmed by the remaining workload, Mr. Watterson told employees this week.

Former crew schedulers working in other areas of the business stepped in to triage inbound phone calls, according to an internal memo Wednesday from

Lee Kinnebrew,

Southwest’s vice president of flight operations, and

Brendan Conlon,

vice president of crew scheduling. Other employee groups were being trained to support overwhelmed schedulers.

Mr. Watterson said the “volunteer army” has been trained on systems and could be called on to pitch in again if the airline begins to see signs that current technology is becoming overwhelmed, as it works on broader fixes. Airline executives said they are confident that existing technology systems can handle the airline’s normal operations while it works on a plan to update them.

Southwest’s ground-operations staff worked to scan thousands of missing bags to figure out where they had ended up. The airline set up new call centers to investigate lost items and update customers, Mr. Kinnebrew and Mr. Conlon wrote. The final step was to coordinate with FedEx Corp. and other delivery companies to truck bags between airports and reduce the strain on Southwest’s remaining flights this week, they wrote.

Running a smaller schedule introduced some new technical challenges, executives said. Planes can’t stay parked for long before they need to be put into short- or long-term storage, so the airline had to rotate through its fleet to ensure that aircraft weren’t sitting idle too long. Maintenance workers had to fan out to different locations to perform checks and regular work on planes that weren’t in their usual locations,

Kurt Kinder,

vice president of maintenance operations, wrote to employees Wednesday.

Write to Alison Sider at alison.sider@wsj.com