Southwest Airlines expects it will have to remove the grounded Boeing Co. 737 MAX jets from its flying schedule beyond the current Oct. 1 re-entry date following the discovery of a fresh safety issue, Chief Executive Gary Kelly told employees on Monday.

Last week, Boeing said that it would take until at least September to solve 737 MAX software issues - later than airlines had been expecting - after U.S. aviation regulators uncovered a new problem during simulator sessions.

"I'm sure this will cause us to have to take the MAX out of the schedule beyond Oct. 1," Kelly said in an internal update, adding that the company would also see "what other modifications we might need to make our plans for this year because it's obviously extending well beyond what I had hoped."

Kelly did not elaborate on the possible modifications. So far, the Texas-based airline has tried to substitute its MAX routes with spare aircraft but has still been forced to cancel about 115 daily flights.

American Airlines Group and United Airlines Holdings , the other two U.S. carriers that operate the 737 MAX, have removed the jetliner from their flying schedules until early September.

The three airlines are expected to provide more details on the financial toll of a prolonged MAX grounding during second quarter results later in July.

Boeing's fast-selling narrowbody was grounded worldwide in March following two deadly crashes within five months.