Boeing shares fell 2.1 percent on Tuesday on concerns related to the first crash of the newest version of the plane-maker's best-selling jet, in which all 189 people on board were killed when it dived into the sea.
Indonesian investigators said on Monday a system designed to deal with the accident scenario was not described in the flight manual. They called for more training for 737 MAX pilots.
U.S. pilot unions later said they were not aware of the new anti-stall system.
Operating procedures and training for the 737 MAX could also change as the FAA and Boeing learn more from the investigation, the regulator said in a statement.
Investigators are preparing to publish their preliminary report on the crash on Nov. 28 or Nov. 29, one month after the Lion Air jet crashed at high speed into the Java Sea.
Until now, public attention has focused mainly on potential maintenance problems including a faulty sensor for the 'angle of attack,' a vital piece of data needed to help the aircraft fly at the right angle to the currents of air and prevent a stall.
The focus of the investigation appears to be expanding to the clarity of U.S.-approved procedures to help pilots prevent the 737 MAX from over-reacting to such a data loss, and methods for training them.
Information recovered from the jet's data recorder last week led the FAA to issue an emergency directive warning pilots that a computer on the 737 MAX could force the plane to descend sharply for up to 10 seconds even in manual flight, making it difficult for a pilot to control the aircraft.
Pilots can stop this automated response by pressing two buttons if the system behaves unexpectedly, the directive said.
But questions have been raised about how well pilots are prepared for such an automatic reaction and how much time they have to respond.
Boeing Chief Executive Dennis Muilenburg told Fox Business Network on Tuesday that Boeing provides "all of the information that's needed to safely fly our airplanes" and that the 737 MAX was a "very safe" airplane.
"This comes out of thousands of hours of testing and evaluating and simulating and providing the information that our pilots need to operate our airplanes safely," Muilenburg said.
"In certain failure modes, if there's an inaccurate angle of attack sensor feeding information to the airplane, there's a procedure to handle that," he added.
The FAA on Tuesday denied a report that it had launched a new probe into the safety analyses carried out by Boeing on the 737 MAX.
Boeing, the world's largest plane-maker, said earlier on Tuesday it delivered 43 of its 737 aircraft last month, up from 37 a year ago, helped by a booming global market.
The number of 737 deliveries was down slightly from the 61 delivered in September due to lingering supplier problems, flagged by a Boeing executive last week.
(David Shepardson in Washington, Sanjana Shivdas in Bengaluru and Eric M. Johnson in Seattle)