CHICAGO (CBS/AP) — Boeing has begun software update testing on dozens of 737 Max jets to make sure the planes are safe to fly, after the entire fleet was grounded because of two fatal crashes in five months.

The aircraft manufacturer has made 96 flights to test a software update for the anti-stall system believed to have played a role in the Lion Air crash in Indonesia in October and the Ethiopian Airlines crash in March.

Boeing CEO Dennis Mulienburg spoke Thursday at a leadership forum in Dallas, where he described the past few weeks as heart-wrenching, with the 346 lives lost in the two crashes.

Officials believe, in both deadly crashes, faulty information from a sensor caused the anti-stall software to push the nose of the plane down. Pilots followed Boeing’s procedures for that situation, but couldn’t regain control of the plane.

Mulienburg said Boeing has met with pilots and officials from the airlines that own 737 Max aircraft, and has made 96 flights totaling 159 flying hours to test a software update for the anti-stall system.

It’s unclear when the software testing will be completed. The FAA and regulators around the world last month grounded all 737 Max jets until they are deemed safe to fly.

The FAA, which will consider whether the plane can resume flying in the U.S., plans to meet Friday with safety officials and pilots from American, Southwest and United, the three U.S. carriers that were using the Max jet.

An FAA spokesman said the agency wants to hear from the airlines and pilots before deciding what Boeing must do before the plane is allowed to fly.

Regulators in Europe and China are conducting their own reviews of the plane, and company insiders and analysts expect foreign regulators to take longer than the FAA to approve the Max’s return to service.

Meantime, U.S. Sen. Edward Markey (D-Massachusetts) and other Senate Democrats have introduced legislation to address safety concerns by requiring aircraft manufacturers to provide airlines with all safety equipment for free.

A warning light for malfunctions in the 737 Max anti-stall system had been sold as an optional extra before the planes were grounded, and neither the Lion Air jet nor the Ethiopian Airlines aircraft had the feature. Markey said if the warning system had been installed on the Lion Air and Ethiopian Airlines planes, the crashes might have been avoided.

The Air Line Pilots Association has endorsed the legislation.

A Boeing spokesman said the company’s planes are equipped with “all critical features” necessary for safety. Boeing has said it will provide the two displays free of charge in the future.