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Southwest Airlines says it has 'stabilized' glitch that led to flight delays

A Southwest Airlines representative told CNBC that a glitch has been "stabilized" on Monday morning.

A statement from the company read:

After a challenging Sunday for our Employees and Customers, we're expecting the technical systems that power our Customer Service to perform normally today. Teams worked throughout the night in advance of our first departures to ensure the smoothest operation today.

The airline carrier experienced a system glitch on Sunday that resulted in about 500 delayed flights. Southwest said that it still has some "additional work to do today to get bags delivered and some delayed or displaced Customers into open seats. We have teams working as quickly as possible to accomplish that."

Shares of Southwest Airlines were higher in premarket trading following the announcement. (Get the latest quote here.)

Flexibility offered to affected travelers on Sunday will extended through Monday, the company said. "We continue to recommend that Customers check-in online or on our app before reaching the airport, and that they present a printed or mobile boarding pass to check luggage, proceed through security screening, and reach the boarding door of our gates," Southwest said in the statement.