Southwest canceled more than 2,800 flights Monday — the day after Christmas — and around 2,600 Tuesday, according to tracking website FlightAware.
Casey Murray, president of the Southwest Airlines Pilots Association, said Southwest had not adequately prepared flights for the storm.
Travelers wait in line near the Southwest Airlines ticketing counter at Nashville International Airport, in Nashville, Tenn., on Tuesday.
Buttigieg said Southwest has pledged to take care of impacted customers, and that the Transportation Department will be holding the airline accountable for that.
Another 2,478 Southwest flights scheduled for Wednesday have also been cancelled, according to FlightAware.