A judge has ruled that Boeing's board of directors must face a lawsuit from shareholders over two fatal 737 MAX jet crashes that killed 346 people in less than six months.

Judge Morgan Zurn of the Delaware Court of Chancery ruled on Tuesday that shareholders can pursue some of their claims against Boeing's board, and she dismissed some of their other claims, Reuters reported.

"That the board knowingly fell short is also evident in the board's public crowing about taking specific actions to monitor safety that it did not actually perform," the ruling said.

Zurn also said that Boeing "publicly lied about if and how it monitored the 737 MAX's safety".

She said Boeing had ignored problems with the plane after the first crash, by a Lion Air jet in Indonesia in October 2018, which killed all 189 people on board.

She said that crash showed a "red flag" about a key safety system on the planes "that the board should have heeded but instead ignored".

A second plane, operated by Ethiopian Airlines, then crashed in March 2019, killing all 157 on board.

Boeing said it was "disappointed in the court's decision to allow the plaintiffs' case to proceed past this preliminary stage of litigation. We will review the opinion closely over the coming days as we consider next steps."

Brian Quinn, a professor at Boston College Law School, said the ruling clears the way for additional discovery and potentially a trial, although he considered that very unlikely.

"Right now everything is lining up where the board of directors are telling their attorneys I don't want to go to trial. You need to pay them whatever it costs, and I cannot as a director admit liability," he told Reuters.

The 737 MAX planes were then grounded around the world. An automated flight-control system known as MCAS was implicated in both crashes, due to a bad sensor. 

The US Federal Aviation Administration cleared the MAX aircraft last November to resume commercial flight after Boeing fixed the flawed design and made other modifications to flight-control computers.

In January, Boeing was charged by the US Justice Department with fraud conspiracy over the 737 MAX and agreed to a deferred prosecution agreement and settlement worth more than $2.5 billion.

The judge's opinion also cited comments by Dave Calhoun, then lead Boeing director, who became Boeing CEO in January 2020 after the board ousted CEO Dennis Muilenburg.

She cited Calhoun's comments that "the board had been 'notified immediately, as a board broadly', after the Lion Air crash and met 'very, very quickly' thereafter".

It added that after the second crash of an Ethiopian Airlines 737 MAX in March 2019, Calhoun represented that the board met within 24 hours of the crash to discuss potentially grounding the 737 MAX.

"Each of Calhoun's representations was false," Zurn said.

She acknowledged the primary victims of Boeing's lax oversight were the passengers of the two 737 MAX flights and their families.

"While it may seem callous in the face of their losses, corporate law recognizes another set of victims: Boeing as an enterprise, and its stockholders," the judge said. "The crashes caused the company and its investors to lose billions of dollars in value."

Reuters and Bloomberg contributed to this story.