The announcement comes after the airline Airlines canceled more flights Thursday and more than 15,000 cancellations since last Wednesday.
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"We are encouraged by the progress we've made to realign Crew, their schedules, and our fleet," the airline said in a press release. "With another holiday weekend full of important connections for our valued Customers and Employees, we are eager to return to a state of normalcy."
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At Midway Airport, piles of bags were moved from the luggage area. The Chicago Department of Aviation says the baggage has been moved to a secured facility.
Southwest has already canceled more than 2,300 flights nationwide for Thursday.
The airline has also increased their operations about 20 percent in the last two days and is expected to be at 100 percent by this weekend.
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Southwest also told the city the company is planning on reimbursing people whose flights were disrupted between Christmas Eve and this coming Monday.
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Refund requests can be submitted through the company's website.
Transportation Secretary Pete Buttigieg said the federal government will "ensure" Southwest Airlines complies with its refund obligations for flights it cancelled over the Christmas holiday.
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"Under the law, Southwest must provide prompt refunds when a carrier cancels a passenger's flight or makes a significant change in the flight, regardless of the reason, unless the passenger accepts rebooking," Buttigieg said in a letter to Southwest CEO Bob Jordan. "This means Southwest must provide refunds within seven business days if a passenger paid by credit card, and within 20 days if a passenger paid by cash, check, or other means."
READ FULL LETTER HERE
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Southwest executives said Thursday refunds and reimbursements are already taking place, but would take weeks to clear the backlog.
In a video, Buttigieg said the department is getting "thousands" of complaints regarding the Southwest meltdown.
"We will penalize Southwest, as we would any airline, to the tune potentially of tens of thousands of dollars per violation if they fail to meet what is required of them to take care of passengers," the secretary said.
The airline also posted a video on Tuesday evening featuring CEO Bob Jordan.
"We're doing everything we can to return to normal operation," Jordan said in the video.