An American Airlines Boeing 737 Max 8 arriving from Washington's Ronald Reagan National Airport is seen taxiing to its gate at the Miami International Airport on March 12, 2019 in Miami, Florida.

American Airlines is prepared to further delay returning the Boeing 737 Max to its schedule as regulators review the manufacturer's safety updates before they allow the planes to fly again, a process that depends on political factors, the airline's CEO, Doug Parker, told employees.

The popular Boeing jet has been grounded worldwide since mid-March after two fatal crashes ⁠— one in Indonesia in October and another in Ethiopia in March ⁠— claimed a total of 346 lives.

The grounding has forced airlines that operate the 737 Max to cancel thousands of flights and sent carriers' schedulers scrambling to find ways to meet peak summer travel demand.

Boeing, which is trying to restore the trust of customers and the flying public, has completed a software fix for the planes after investigators implicated an anti-stall program in both crashes. Regulators, including the Federal Aviation Administration, have not yet approved the software changes or the additional pilot training material Boeing has been developing.

"There is an absolute software fix that's this close to being certified, but they've been saying that for a while," Parker told employees in a town hall meeting last week, according to an audio recording of the event that was reviewed by CNBC. "I think as much as anything now it may be politics as much as the true certification ... safety issue. I don't think the FAA wants to be alone in doing this."

The U.S. was the last major aviation market to ground the jets in March after the Ethiopian Airlines crash, a stark change for the agency that has historically taken the lead on aviation safety.

The FAA's acting chief Daniel Elwell has expressed hope that international aviation regulators and the agency could work together to get the planes flying again. Boeing said it is addressing additional questions from the regulator and will schedule a certification test flight once those are answered.

American Airlines earlier this month said it would remove the 737 Max from its schedule until after Labor Day, more than two weeks later than it had previously said. The removal of the plane will lead to the cancellation of about 115 flights a day. The carrier has 24 Boeing 737 Max planes in its fleet of more than 900 aircraft. Southwest Airlines and United Airlines have also delayed the planes' return to their schedules.

Even after officials approve the plane for service American will need about 30 to 45 days to provide its more than 4,000 Boeing 737 pilots with the additional required training.

While some pilots may be prepared to fly on the jet shortly after its approved by regulators, because airlines frequently swap out airplanes and crews, a flight could be left without pilots that have been trained, so it is easier for airlines to delay its return to service.

Because American's crews need to start picking trips for their schedules in September in the coming weeks, the airline may have to push out the reintroduction to October, Parker said.

"You may see us push it back a month," Parker told employees, adding that an additional delay would likely be announced in early or mid-July.

Parker told an investors earlier this month that pilots and executives would likely fly on the plane before passengers.

The president of American Airlines pilots' union on Thursday wrote to Boeing's CEO Dennis Muilenburg, requesting access to a full-motion 737 Max simulator that the manufacturer has in Miami, the only one of its kind currently in the U.S., before the planes are re-certified by regulators. The union has been highly critical of Boeing, saying it did not inform the pilots of the additional software in the plane until after the first crash, in Indonesia, in October and expressed safety concerns before a House aviation panel last week.

Boeing said it would work with the union's incoming president "to schedule his time in the full-motion simulator in the near future."