The grounding will amount to about 115 cancelled flights per day through Aug. 19, or about 1.5% of American's total flights each day this summer.
"We are highly confident that the MAX will be recertified prior to this time," American Airlines CEO Doug Parker said in the letter. "But by extending our cancellations through the summer, we can plan more reliably for the peak travel season."
Boeing, which manufactures the 737 Max 8 and Max 9, continues to work on a software fix for the grounded jets that will be certified by the Federal Aviation Administration.
A preliminary report issued in early April showed the Ethiopian Airlines jet that crashed on March 10 suffered a damaged sensor that caused the jet's horizontal stabilizer system to kick in. Despite initially turning the system off, the pilot later turned it back on and the jet nosedived into the ground. A malfunctioning horizontal stabilizer system also caused a Lion Air flight to crash last October.
U.S. Secretary of Transportation Elaine Chao assured members of Congress on Wednesday that once the FAA receives Boeing's proposed software enhancements for the 737 Max MCAS function "it will be thoroughly reviewed to ensure the solution has addressed all pertinent issues."
"Let me emphasize that the FAA will not approve Boeing's proposed changes until the FAA is satisfied that it safe, and preserve the preeminence of the United States as a gold standard in aviation safety," Chao said during a House Appropriations Committee hearing.
Parker emphasized his concern for safety in the letter, saying, "Families everywhere are counting on American Airlines for their summer vacations, family reunions, trips to visit friends and adventures overseas. Our commitment to each other and to our customers is to operate the safest and most reliable operation in our history."
All 737 Max jets were grounded on March 13 by the FAA, in an announcement by President Donald Trump, in the wake of two crashes in six months -- one last October off the coast of Indonesia and another in March in Ethiopia. A total of 346 people were killed in the two accidents. The FAA and U.S. carriers had held off on grounding the 737 Max even as other countries around the world did so. The U.S. finally relented days later.
American Airlines joined Southwest in announcing it would ground the 737s through August. Southwest announced its decision to ground Max jets through Aug. 5 last week.
American Airlines had previously announced on April 7 that it would cancel approximately 90 flights per day through June 5, "in an effort to provide more certainty and avoid last minute flight disruptions.” The announcement Sunday extends that order.
The airline warned investors last week that the grounded jets were likely to impact first quarter revenue.
"The company now expects its first quarter total revenue per available seat mile (TRASM) to be approximately flat to up 1.0 percent year-over-year vs. its previous guidance of flat to up 2.0 percent," American Airlines said in a Securities and Exchange Commission filing. "This change is due primarily to the impact of the government shutdown, the grounding of the company’s MAX fleet, and the removal from service of the 14 737-800 aircraft."
American is the second-largest operator of 737 Max 8s in the U.S., behind Southwest.
ABC News' Christine Theodorou, Christina Carrega and Mark Osborne contributed to this report.