Southwest Airlines promised to reimburse passengers for expenses such as hotels and car rentals in addition to refunding tickets after it canceled thousands of flights due to a massive winter storm and said there would be a still-undetermined hit to its earnings.

"There'll certainly be an impact to the fourth quarter," Chief Commercial Officer Ryan Green told reporters on a call on Thursday. "We're ... working through all the financial elements of this. We'll share that information when we have all that compiled and are ready to do that."

Some analysts estimate the meltdown could shave as much as 9% off Southwest's fourth-quarter earnings.

Company executives on the call declined to estimate the number of travelers affected by the disruptions since Friday.

While other U.S. airlines got back to their feet relatively quickly, Dallas-based Southwest is still limping back to normalcy. The carrier has canceled at least 16,000 flights in the past week, including roughly 60% of all scheduled flights on Thursday, according to data from flight tracker FlightAware.

"If you had to make alternative travel arrangements like hotels, meals, rental cars, gas for rental car, those will qualify for reimbursements," Green said, adding that it would take several weeks for the repayments.

Friday cancellations are expected to drop drastically, with Southwest saying it was "eager to return to a state of normalcy" ahead of the New Year holiday weekend.

Just two months ago, Southwest had forecast "strong" earnings in the fourth quarter and had estimated a 13% to 17% jump in operating revenue.

The bitter weather was just part of the problem for Southwest. Its dated technology failed to map crew to flights and its point-to-point operational structure created chaos for schedules, the company has admitted and union members have said.

The U.S. government has called the airline's meltdown a system failure and vowed action.

In a letter to Southwest chief Bob Jordan on Thursday, Transportation Secretary Pete Buttigieg warned that the company would be held accountable if it did not fulfill commitments to customers for "controllable delays and cancellations."

The company has been eager to show it is turning the page on the debacle, which sent its stock price tumbling. Southwest shares on Thursday closed up 3.7% as Wall Street rose broadly, the first day of gains since last Friday.

Jordan apologized for the disruption and said the process to reposition crew and aircraft following the storms had been a "manual process" that has taken time, and a "volunteer army" made up of salaried employees at the company's headquarters was helping.

"I cannot imagine that this doesn't drive changes to the plan" to modernize the airline's operations, Jordan said, adding that technology improvements were under way but it was a "large and complicated process."

Employee unions say they have repeatedly warned Southwest management that the airline's technology systems badly needed upgrades.

Flight attendants have been complaining about technological failures at the airline for years, according to Lyn Montgomery, president of the Southwest Airlines Flight Attendants Union, a local 556 of the Transport Workers Union.

"There's many ways it could have been avoided," Montgomery said on Thursday on CNN, saying that could have included commitments by Southwest executives to ensure that IT infrastructure would be able to meet the carrier's growth.

The comments echoed those of the Southwest Airlines Pilots Association, which said leadership had failed to adapt operations to address repeated systems failures, despite years of calls for improvements by the union.

Improvements it called for included changes to crew scheduling software and communication tools that would have allowed displaced crews to remain in contact with the company.