“I stand with you and your team in continuing to move at the pace of safety,” Mr. Dickson said. Mr. Bahrami, who formerly worked for a trade group that advocated for Boeing, distributed the letter to F.A.A. employees working on the Max approval.

Boeing has encountered repeated delays and setbacks in its efforts to get the Max flying again. The company has been preparing the software fix since October 2018, when the first Max crashed in Indonesia after a new system, known as MCAS, sent the plane into a nose dive. Governments around the world grounded the plane in March, after a crash in Ethiopia involving the same system.

Another delay occurred in recent weeks when engineers and international regulators who had gathered at the Cedar Rapids, Iowa, offices of Collins Aerospace, a Boeing contractor, were reviewing the software update. European regulators wanted the information about the software presented in a different format from the one Boeing had prepared, creating another hurdle, according to two people familiar with the delay.

“We are working closely with the F.A.A. and other regulatory authorities as we work towards certification and safe return to commercial service,” Boeing said in a statement on Friday. “As we have said, the F.A.A. and other regulatory authorities will determine the timing of certification and return to commercial service.”

A key step toward meeting Boeing’s timeline of approval in December is evaluating how pilots respond to failures of the system in a simulator. In conversations with the F.A.A., company executives including Mike Sinnett have argued that it’s legitimate to have pilots start testing the new software, which they maintain is essentially complete.

“We have been unequivocal in all of our conversations with leaders at Boeing that safety is the F.A.A.’s top priority,” the agency spokesman Lynn Lunsford said in a statement on Thursday. “We will take all the time we need to thoroughly evaluate Boeing’s proposed changes to the 737 Max to ensure it can safely return to service.”

Boeing has been producing the Max jets at a reduced rate for months and has hundreds in storage. Airlines want to begin receiving the planes as soon as possible so they can begin the lengthy process of getting them ready to fly again. The three airlines that fly the Max in the United States — American Airlines, Southwest Airlines and United Airlines — have all canceled Max flights into March.