The airline had been working to a 19 August timetable, but has now extended this to 3 September while Boeing works on a software update.
It means cancellations of approximately 115 American Airlines flights a day will continue into early September.
The 737 Max was grounded globally in March following a second fatal crash involving the airline in five months.
Last October, Lion Air flight 610 crashed into the Java Sea shortly after taking off from Jakarta, killing all 189 people onboard.
Then in March, Ethiopian Airlines flight 302 came down en route to Nairobi. All 157 people onboard died.
Boeing is working on a software fix for a deep-seated control system understood to have been active when both crashes occurred.
“American Airlines remains confident impending software updates to the Boeing 737 Max, along with new training elements Boeing is developing in coordination with our union partners, will lead to recertification of the aircraft soon,” said the airline in a statement, adding it had been in “continuous contact” with the relevant authorities in the US.
“Our reservations and sales teams will continue to work closely with customers who are impacted by these cancellations.”
While it has long been established Boeing has been working on a software fix, the company is yet to submit the fix to the US Federal Aviation Administration for approval, meaning the process to update the near-400 grounded 737 Max aircraft is still yet to get under way.
Iata has predicted the aircraft may not resume service until late August, with American Airlines now revising its programme back to September.
The process has already hampered Tui’s summer 2019 flight programme, with its airline operating 15 of the Boeing aircraft, although it has pledged to ensure all holidays will go ahead as planned irrespective of the issues with the 737 Max.
Tui has forecast a €300 million hit if the aircraft remains unavailable for the entire summer.
Norwegian, meanwhile, operates 18 737 Maxs, although none of these currently operate to the UK. It has adjusted and combined some transatlantic flight schedules to reposition parts of its fleet to mitigate the grounding.
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