The Justice Department is considering whether to revive a criminal charge of fraud against Boeing laid in 2021, that was linked to the two crashes.
The charge has laid dormant since the company acknowledged in a settlement that it had mislead air-safety regulators about aspects if the 737 Max, and promised to create a new compliance system to detect and prevent further fraud.
Last month, prosecutors determined that the settlement was violated when a door panel flew off a 737 Max plane during an Alaska Airlines flight in January, leaving a gaping hole in the fuselage mid-flight.
The Justice Department has until 7 July decide whether to revive the case.
In the letter, Mr Cassell said his clients recommended that the department order a portion of any future fine to be used to create an independent monitor of the company’s safety and compliance measures.
Families of those killed in the crashes attended Tuesday’s hearing in Congress and held up photographs of loved ones.
“I flew from England to Washington DC to hear in person what the Boeing CEO has to say to the Senate and to the world about any safety improvements made at that corporation,” said Zipporah Kuria, whose father was killed in the 2019 crash of a Boeing 737 MAX 8 jet.
“I also continue to press the US government to hold Boeing and its corporate executives criminally responsible for the deaths of 346 people. We will not rest until we see justice.”