A Boeing 737 MAX 8 for China Southern Airlines (front) is pictured at the Boeing Renton Factory in Renton, Washington on March 12, 2019.

The draft report from the FAA 's Flight Standardization Board recommends that pilots take additional computer-based training for the MCAS automated flight system.

The Federal Aviation Administration on Tuesday released its initial review of Boeing's update to its 737 Max anti-stall software suspected of contributing to two fatal plane crashes, calling it "operationally suitable."

The company's shares jumped by about 2% on the news.

Boeing said it's completed 96 flights totaling over 159 hours of air time with its software fix for the Max jet. The company is also updating airlines by bringing representatives into flight simulators and showing them the modified flight control system.

The company has stopped deliveries and has cut Max production by 20% as it works on a fix. The jets have been grounded since mid-March. Wells Fargo said Tuesday that Boeing's troubles with the Max will reduce second-quarter GDP growth by 0.2%.

Separately, Institutional Shareholder Services on Tuesday recommended that shareholders vote in favor of a proposal that would require Boeing to have an independent chairman of the board. That title is currently held by CEO Dennis Muilenburg.