Washington (CNN) A senior Boeing engineer filed an internal ethics complaint this year following two fatal 737 Max crashes, claiming that the company rejected a safety system during the plane's development to cut costs though it could have reduced the risks, according to the New York Times.

In the complaint, which Boeing has sent to the Justice Department, the engineer Curtis Ewbank alleged, "Boeing management was more concerned with cost and schedule than safety or quality," according to the newspaper, which has reviewed the complaint.

"I was willing to stand up for safety and quality, but was unable to actually have an effect in those areas," Ewbank said in the complaint, the Times reported.

Ewbank also called out Boeing's chief executive Dennis Muilenburg for publicly misrepresenting the safety of the plane, the newspaper reported.

Muilenburg is set to speak to the New York Economic Club Wednesday afternoon.

Read More