The airline hoped to bounce back partly by reducing its load -- Southwest canceled more than 220 flights, or about 5 percent of its schedule, early on Thursday.
Southwest said it canceled nearly 700 flights Wednesday and "hundreds more" were delayed -- tracking service FlightStats Inc. put the delays at nearly 2,100.
The airline said "most systems are back online" after problems that began with an outage Wednesday afternoon and continued intermittently well into the night.
"We know we disappointed customers today. We are really, really sorry about that," spokeswoman Linda Rutherford said in a video that the airline posted Wednesday night. "That is unacceptable to us."
The airline said that it was trying to accommodate stranded passengers on new flights. Because of that, it expected long lines and told passengers to arrive early for Thursday flights.
Southwest officials said they had not identified the cause of the outage. Several of the airline's technology systems were affected for several hours. The airline briefly held up all departing flights on Wednesday, and its website and electronic check-in systems failed.
The airline put out this statement: "Thank you for your patience today as we recover from yesterday’s technology outage. Southwest.com
has been restored with full functionality and is available for your travel needs."
After a similar outage last October resulted in 800 delayed flights, Southwest blamed a faulty software application.