An American Airlines Boeing 737 MAX 8 flight from Los Angeles lands at Reagan National Airport shortly after an announcement was made by the FAA that the planes were being grounded by the United States in Washington, March 13, 2019.

The Federal Aviation Administration, already under the gun for how it has handled the growing controversy surrounding the Boeing 737 Max, says reviewing a possible software fix for the grounded airplanes is "an agency priority."

Boeing has been working on a software update that is expected to correct issues with the 737 Max maneuvering characteristics augmentation system. That system, which can push the nose of a 737 Max lower to avoid a stall, is suspected as being a contributing factor in the crash of a Lion Air jet last October.

In an update to industry guidance called the Continued Airworthiness Notification to the International Community, or CANIC, the FAA said:

"Boeing is developing a service bulletin that would specify the installation of new flight control computer operational program software. Boeing has also developed flight crew training related to this software. The FAA's ongoing review of this software installation and training is an agency priority, as will be the roll-out of any software, training, or other measures to operators of the 737 Max."

Boeing is hoping to have the new software finalized by March 25, according to a person familiar with the matter, but it will not issue the updated software to airlines until it's been approved by the FAA. Separately, it's unclear if the new software and updated training for 737 Max flight crews will be enough to prompt the agency to lift the grounding of the Boeing jets. Both Canadian and European aviation authorities have indicated they plan to review any 737 Max software updates themselves before approving the Max to return to the skies in Canada or Europe.

Meanwhile, the FAA says it continues to review information from the cockpit voice recorder and flight data recorder of an Ethiopian Airlines 737 Max that crashed on March 10.

"Understanding the circumstances that contributed to this accident is critical in developing further actions and returning aircraft to service," the FAA said in its updated CANIC.

Shares of Boeing fell in after-market trading Wednesday on news that the FBI has reportedly joined in a criminal investigation of the certification process for the company's 737 Max jets, two of which have crashed since October killing 346 people.

The Seattle Times reported that the agency is assisting federal aviation investigators in a federal grand jury probe based in Washington, D.C. looking into the process. Boeing's shares were down less than 1 percent.

The news comes after the Department of Transportation on Tuesday asked the agency's watchdog to audit the Federal Aviation Administration's approval of Boeing's 737 Max 8 aircraft.