Consumer advocate Ralph Nader on Monday called for the removal of Boeing CEO Dennis Muilenburg and the entire Boeing board of directors as the fallout intensifies over the aircraft maker's grounded 737 Max.

"It's not happening at Boeing because the people at the top are in the same pit together," said Nader, whose grandniece was killed in the March crash of a 737 Max jet in Ethiopia. "They don't want to admit that they really, really performed in a very seriously adverse way to the safety of airline passengers."

Muilenburg was stripped of his chairman title, the company announced Oct. 11. Boeing said the separation of the two roles will allow Muilenburg to focus on getting the Max back to service. Lead director David Calhoun will serve as nonexecutive chairman.

"That's the first crack," Nader, who was speaking on CNBC's "Squawk Box," said of splitting the chairman and CEO.

Boeing was not immediately available to respond to CNBC's request for comment on Nader's remarks.

Shares of Boeing fell by more than 5% in Monday morning trading before regaining some ground, after Friday's revelations of 2016 messages that called into question the safety of the 737 Max jet's flight control system. Boeing said Sunday that it understands the concerns over the test pilot's leaked messages and that it's continuing to investigate what they meant.