Boeing said Thursday that it has completed its software fix on the 737 Max, a key step toward getting the grounded jetliner back in the air after two deadly crashes.

But the jet still isn't likely to be back in service for months. It now faces tests and certification by the Federal Aviation Administration and other agencies around the world.

The software update focuses on the automated system designed to counteract a tendency for the plane's nose to point up due to heavier engines mounted in a more forward position on the wing than previous 737 versions.

The system, the Maneuvering Characteristics Augmentation System (MCAS), played a role in the crash of 737 Max jets operated by Lion Air in October and by Ethiopian Airlines in March. The two crashes claimed a total of 346 lives. The pilots of both jets wrestled trying to keep their planes in the air as the system repeatedly kept pushing the nose toward the ground.

Boeing has said it is redesigning the software so that pilots can more easily shut off the system, keeping it from repeatedly reengaging, and not making it react as dramatically in pushing down the nose. Rather than relying on data from a single sensor, the new system will take a measure of both sensors that tell the MCAS system whether the nose is pointed too high.

Boeing said it has flown 207 test flights comprising 360 hours of flight time in 737 Max jets with the new MCAS software.

The FAA has asked for information on how pilots will interact with cockpit controls and displays in different flight scenarios with the new software, Boeing said in a statement. After submitting answers to those queries, Boeing said it plans to start certification flight tests.

“We’re committed to providing the FAA and global regulators all the information they need, and to getting it right," said Boeing CEO Dennis Muilenburg in a statement. "We’re making clear and steady progress and are confident that the 737 Max with updated MCAS software will be one of the safest airplanes ever to fly."

The Max has been in service around the world with thousands of planes on order. Some airlines, which have put all their Max jets in storage, are not counting on them being back in the air until the fall, although no formal schedule has been announced. In the US, Southwest and American are airlines with substantial numbers of Max planes in their fleets.

Acting FAA administrator Daniel Elwell said at a hearing Wednesday that the Max will return to service "only when the FAA's analysis of the factual and technical data indicates it is safe to do so." It is yet to be seen whether international counterparts to the FAA act with the same speed as U.S. regulators.