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.