The company said in a statement Sunday that the roughly 40 flights it had canceled accounted for about 1 percent of its 4,000 scheduled flights that day.
The airline would not detail how many flights were canceled on Monday morning.
"Since our operational plans entail multiple aircraft entering and exiting scheduled service during the ongoing inspection period, we are not able to provide real-time, continuous updates on total flight disruptions," Southwest said in a statement to the media.
"Again, we are working directly with impacted customers on the minimal flight changes as we work diligently to ensure the safety of our fleet."
Southwest passengers face cancellations, delays due to engine inspections 02:17 As of 10:30 a.m. ET on Monday, the travel-tracking website FlightAware showed that Southwest had canceled 128 flights, or 3 percent of its total, but it was unclear how many of those cancellations were specifically because of engine inspections.
A spokesperson for FlightAware told the media that Southwest typically averages a few dozen cancellations on a normal day — making 128 above the average.
There were no major weather events across the country on Monday morning apart from some heavy rains over the Southeast.
The emergency inspections come after passenger Jennifer Riordan died aboard a flight last Tuesday when she was partially sucked out of the plane following an engine explosion that shattered a window.
The flight from New York was forced to make an emergency landing in Philadelphia.
Southwest said after the accident that all of the CFM56-7B engines on its Boeing 737 fleet will be reviewed within 30 days.
“When we announced the accelerated engine fan blade inspection program on Tuesday night, we said there would be some impact on our operation,” the airline said in its Sunday statement.
“We have minimized flight disruptions this past week through actions such as proactive aircraft routings to cover open trips, performing inspections overnight, and utilizing spare aircraft, when available.”
The company said the cancellations were not because of a Friday directive by the Federal Aviation Administration and European airline regulators ordering emergency inspections for fan blades on certain CFM56-7B engines within 20 days for all airlines.
The “emergency airworthiness directive” affects 352 engines in the U.S. and 681 engines worldwide, according to the FAA.
“The cancellations are a result of our voluntary, accelerated engine fan blade inspection program announced on Tuesday night,” the airline said.