The China Air Transport Association said in a statement Friday that the groundings and delayed deliveries of the planes were causing "serious damage" to the companies' businesses.
It estimated their losses at 4 billion yuan (USD 580 million) should the planes remain grounded through the end of next month.
The group said it would "actively support and coordinate member companies to carry out their compensation work."
It was unclear if the push to penalise the American aircraft maker over losses resulting from the grounding of the aircraft was in any way linked to trade tensions between Beijing and Washington.
The Chinese airlines, including major carriers Air China, China Eastern and China Southern, have 96 Max aircraft in their fleets, with more than 30 more due to be delivered this year.
The company has not yet submitted a final, formal application for approval of its update to a flight-control system that has been implicated in the crashes.
That submission will be followed by test flights to demonstrate the changes to FAA experts.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)