A Southwest Airlines jet sits on the runway at Philadelphia International Airport after it was forced to land with an engine failure, in Philadelphia, Pennsylvania, on April 17, 2018.

The company is in the midst of a fan-blade inspection program that has lead to the cancellation of scores of flights.

CEO Gary Kelly told CNBC in an interview Thursday that "a little bit of softness is to be expected" and noted that the company had pulled all of its marketing and promotions following the incident.

"Approximately one to two points of this estimated decrease is attributable to recent softness in bookings following the Flight 1380 accident," Southwest said.

Southwest Airlines warned on Thursday that reservations have declined in the wake of a deadly in-flight engine failure aboard one of its flights.

A blade on one of the Boeing 737-700's engines broke off when the plane was flying above 30,000 feet, sending shrapnel flying and puncturing a window. The flight for Dallas from New York's LaGuardia Airport an emergency landing in Philadelphia. One passenger, bank executive Jennifer Riordan, was partially sucked out of the opening and died.

It was Southwest's first passenger fatality from an accident in its history and the first such fatality aboard a U.S. airline since 2009.

Last week, U.S. and European regulators mandated more stringent checks on the fan blades of the engine type that malfunctioned on Flight 1380. That came after the engine's manufacturer recommended inspections of fan blades on a larger group of engines than it had called for last year.

CNBC reported Friday that CFM International, maker of the CFM56-7B engine, had been planning to issue such guidance before the incident on Flight 1380.

Kelly said Southwest expects to finish its engine inspections by the end of May and that checks on about 80 percent of its fleet since 2016 have been completed.

"I'm pleased with the results that we're seeing so far," Kelly said.

Southwest is revamping its fleet with a new variety of fuel-efficient Boeing 737s. One new destination that those aircraft will likely serve is Hawaii. Southwest said Thursday that it plans to start selling flights to Hawaii, which it announced last year, sometime in 2018. The airline will fly to the Honolulu International Airport, Lihue Airport, Kona International Airport and and Kahului Airport, Southwest said.