New York (CNN Business) Boeing CEO Dennis Muilenburg warned investors Wednesday that the company might need to further slow or temporarily halt its 737 Max production.

Boeing has continued to build the 737 Max, its bestselling jet, although at a slower pace. The plane has been grounded since mid-March because of two fatal crashes that killed more than 300 people.

Boeing hopes to get approval for the plane to fly again sometime early in the fourth quarter. Muilenburg said any further delays in approval to fly the 737 Max again could jeopardize its production. A further slowdown or temporary shutdown of 737 Max production is "not something we want to do, but an alternative that we have to prepare for," Muilenburg told investors on a conference call. He said the company needs to prepare for that "to make sure we've covered all scenarios."

It is unclear when the 737 Max will be allowed to return to service . Boeing is working on a software fix to a safety system which is believed to have caused the two crashes. But it says it won't be able to present that fix to aviation authorities until September at the earliest, and it hopes to have a certification flight in October.

After the certification flight, Muilenburg said Wednesday he believes regulators will approve the 737 Max for flight in a matter of weeks. So it's possible the plane won't be cleared to fly again until at least late this year.

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