CHICAGO (CBS/AP/CNN) — Boeing’s 737 Max jets won’t be in the air for several more weeks, after the aircraft manufacturer told the FAA it needs more time to work on a software fix, following two deadly airliner crashes in less than five months.

The Chicago-based company’s update to a flight control system suspected of playing a role in the fatal crashes in Indonesia and Ethiopia was expected to be completed last week, but FAA spokesman Greg Martin said Boeing needs more time to make sure it has identified and fixed all of the problems.

An aviation source told CNN that Boeing had discovered “an additional piece to address” in the final review of the new software and that integrating new flight control software on a complex aircraft takes time.

The FAA will conduct another safety review once the 737 Max software is updated. Boeing needs approval not just from FAA, but elsewhere, including Europe and China, where safety officials have indicated they will conduct their own reviews.

All Boeing 737 Max aircraft have been grounded since last month, after a total of 346 people died in Max 8 crashes in Indonesia and Ethiopia.

A preliminary report on the second crash is expected in the next few days, but data from the Indonesian plane indicated pilots unsuccessfully fought the automated anti-stall system for control of the plane, which plunged into the Java Sea shortly after takeoff. According to published reports, the same system activated on the Ethiopian Airlines flight.

Boeing is making changes in an automated system that is designed to prevent the plane’s nose from rising, which can lead to a dangerous aerodynamic stall. The changes include relying on readings from more than one sensor before the anti-stall system activates and pushes the nose down, and making the system’s actions less severe and easier for pilots to handle. Boeing has said it will pay to train pilots on the technology.

Two American Airlines pilots who attended a session with Boeing experts last week expressed satisfaction with the manufacturer’s changes. American’s chief 737 pilot, Roddy Guthrie, said Boeing added “some checks and balances in the system that will make the system much better.”

Congress, meanwhile, is looking into the relationship between Boeing and the FAA. The House Transportation and Infrastructure Committee said Monday that it had requested records from both Boeing and the FAA related to the certification of the 737 Max.

(© Copyright 2019 CBS Broadcasting Inc. All Rights Reserved. The Associated Press and the CNN Wire contributed to this report.)