Southwest had canceled more than 400 flights - 10 percent of its schedule - by midmorning Wednesday.
Chief Operating Officer Mike Van de Ven says the Aircraft Mechanics Fraternal Association has a history of work disruptions and says the airline is considering all options to fix its operations.
The union says that Southwest is "scapegoating" mechanics, and warned that the conflict "does not bode well" for safety at one of the nation's biggest airlines.
Southwest has tangled with the union before - it has two pending lawsuits against it.