Southwest Airlines Co. and American Airlines Group Inc. said they will remove the 737 Max from their flight schedules through early March—almost a year since Boeing Co.’s best-selling jet was grounded worldwide after two deadly crashes.

The plan to pull the plane from Southwest’s schedule through March 6 is due to “continued uncertainty around the timing of Max return to service,” the carrier said in a regulatory filing Friday. American followed suit within hours, saying it expected to resume commercial flights with the aircraft on March 5.

The chief executive officers of both airlines have signaled rising frustration with the worsening delays afflicting the Max, as Boeing seeks to win safety regulators’ approval for the plane to resume flights. The jetliner was grounded March 13, after accidents at Indonesia’s Lion Air and Ethiopian Airlines killed 346 people.

Boeing has targeted this quarter for the narrow-body plane to be cleared to fly again, which requires Federal Aviation Administration approval of new software and other changes meant to avoid a repeat of the disasters. In both crashes, a sensor fed erroneous signals to flight-control software, which repeatedly pushed down the aircraft noses until pilots eventually lost control.

Boeing fell 1.8% to $351 at the close in New York, having extended losses after Southwest’s announcement. The Dallas-based airline fell 0.1% to $58.18, while American dropped 0.4% to $30.76.

After the grounding is lifted, Southwest expects it will need a month or two to return its Max jets to passenger service. While the company has always had an all-Boeing fleet and has tied its future growth to the Max, CEO Gary Kelly said last month that the board would review whether to add other aircraft types.

Southwest parked its 34 Max planes in March, and had been scheduled to receive 41 more this year. The largest Max operator is still targeting seven deliveries of the plane this quarter, with the remaining 34 pushed into 2020. But it said it “offers no assurances that current estimations and timelines are correct.”

The company last month pulled the Max from its schedule through Feb. 8, while American had removed the plane through Jan. 15. United Airlines Holdings Inc. has taken the Max out of its schedule until Jan. 6.

‘Exhibition Flights’

American plans to run “exhibition flights” for airline employees and invited guests from the time the plane is certified until March 5. The Fort Worth, Texas-based carrier, with 24 Max aircraft, will gradually phase in commercial flights through the month.

CEO Doug Parker has said he is committed to making sure Boeing provides compensation “for the damage they caused to American’’ because of the Max’s absence.

“We don’t think that’s a cost that should be borne by the American shareholders,’’ Parker said at a presentation Nov. 6. “It should be borne by the Boeing shareholders because this was their failure not ours.’’