Shares of Boeing fell in after-market trading Wednesday on news that the FBI has reportedly joined 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 bureau 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 department's watchdog to audit the Federal Aviation Administration's approval of Boeing's 737 Max 8 aircraft.

Transportation Secretary Elaine Chao on Tuesday sent a memo to Calvin Scovel, the department's inspector general, formalizing the request.

Boeing and the FAA, which certified the plane two years ago, are under increasing scrutiny after the crash of Ethiopian Airlines Flight 302 on March 10, which went down shortly after takeoff, killing all 157 people on board. Investigators who have extracted data from the airliner's black boxes said they detected "clear similarities" between the Ethiopian Airlines flight and a crash in Indonesia in October that killed all 189 on board.

The FAA said Wednesday that 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 in Indonesia in October.