They were expecting to represent over 50 per cent of those on board MH370, she said. "In the past, we've represented even closer to 100 per cent."
The lawsuit would be filed against the aircraft's manufacturer Boeing, and not Malaysia Airlines, as the law firm believed the cause of the crash was mechanical and equipment failure.
"We do not believe that the plane was hijacked and we do not believe that the pilot or co-pilot crashed the plane purposely."
The FAA had previously identified problems with corrosion and the fuselage in the Boeing 777 fleet, Ms Kelly said.
"So what we think happened is either the cockpit had some problems with the electric system - maybe an electric fire - or maybe there was a sudden loss of cabin pressure and that the pilot and the co-pilot became unconscious and for several hours it was a ghost plane and it crashed after it ran out of fuel."
The firm would withdraw the case if it became clear that the cause of the aircraft's disappearance was due to a hijacking, she said.
"But we do not believe that is the case because we have similar cases in the past where, at the beginning, the investigators [thought] that it was a hijacking or that it was pilot suicide and it turned out that it was not."
Malaysia Airlines took out a full-page advertisement with white type on a black background in today's NZ Herald expressing their "deepest condolences" over the flight's disappearance.
"We are all deeply saddened by the news of MH370. Our sincerest condolences go out to the loved ones of the 239 passengers, friends and colleagues.
"Words alone cannot express out enormous sorrow and pain. They have left us too soon, but they will never be forgotten.
"They will remain forever in our thoughts and prayers."