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UPDATE 3-American Airlines CEO sees Boeing 737 MAX flying by mid-August

By Tracy Rucinski

(Adds details on return to service, Delta CEO comment, shares)

By Tracy Rucinski

CHICAGO, June 12 (Reuters) - The grounded Boeing Co 737 MAX is "highly likely" to be flying by mid-August, American Airlines Group Inc Chief Executive Doug Parker told shareholders on Wednesday.

A battered aviation industry is awaiting regulatory approval for a software fix and pilot training updates by Boeing that would pave the way for the troubled jet to fly again following two deadly crashes in Indonesia and Ethiopia within five months.

American Airlines has said the economic impact of the grounded MAX would be about $350 million between its worldwide grounding in mid-March and Aug. 19, when the airline had initially envisioned flying its 24 MAX jets again.

On Sunday, American extended cancellations of about 115 daily flights until Sept. 3, but Parker said that decision merely reflected monthly scheduling plans for crew.

"No one should take that as some indication that we don't think the aircraft will be ready by Aug 19," Parker said during the company's annual shareholders meeting.

"We wouldn't be selling seats today if we didn't think it was a highly likely possibility (...) that we'd be able to provide that service by Sept. 3," he added.

Boeing has yet to formally submit its software fix to the U.S. Federal Aviation Administration, which said on Wednesday it does not have a specific timetable on when the 737 MAX would return to service.

Still, Parker said he understood there was "an absolute fix" for the 737 MAX, while acknowledging there was no certain timetable and that rebuilding public confidence may take time.

Once regulators approve the MAX, airlines will need some time to train pilots on the software fix, meant to prevent the erroneous triggering of a system called MCAS that played a role in the Lion Air and Ethiopian Airlines crashes, and to prepare the jets following months of storage.

Before the jet flies commercially, Parker said he and other executives would fly in the MAX and noted that if American pilots were comfortable taking up the aircraft, over time, the flying public would recognize that it is safe.

Speaking on CNBC on Wednesday, Delta Air Lines CEO Ed Bastian said he believed consumer confidence would take a while to restore, and that a MAX return to service was "probably going to be longer than anyone would like it to be."

Shares in Delta, which does not operate the MAX, have outperformed those of U.S. rivals with the jets. American shares, which have lost about 4% this year, were up 1.2% on Wednesday. (Reporting by Tracy Rucinski; Additional reporting by Philip George; Editing by Steve Orlofsky and Bernadette Baum)