“Lubitz’s particular history of depression and mental instability made him a suicide time bomb,” Marc S. Moller, a partner at Kreindler & Kreindler, the New York law firm representing the families, said in a statement. “The fuse which culminated in Lubitz’s suicide,” he added, “was lit when A.T.C.A. negligently allowed him to begin commercial pilot training.”

Image Lufthansa has said it was aware of Mr. Lubitz’s history of mental illness, but maintains that it was unaware of its severity. Credit... Foto-Team-Mueller/European Pressphoto Agency

Lufthansa did not respond to requests for comment on Wednesday.

The families’ decision to pursue a civil case in the United States comes amid an inquiry by French prosecutors seeking to assign criminal responsibility for the crash. The investigation has been complicated by strict medical privacy laws in Germany that discouraged Mr. Lubitz’s doctors from alerting regulators or the airline to his deteriorating mental health in the weeks before the crash.

Lufthansa has said that it was aware of Mr. Lubitz’s history of mental illness. But the airline has maintained that it was unaware of its severity and that the decisions to readmit him to its training program — and ultimately to hire him as a pilot — were based on assessments by doctors who found him to be healthy.

Until now, most families of the victims — almost all of whom are European — have received relatively modest offers of compensation from Lufthansa in accordance with their national laws, which vary widely by country. Almost half the crash victims were citizens of Germany, where, under current law, relatives may claim only limited economic damages and are not entitled to compensation for emotional pain and suffering.

A Lufthansa offer to German relatives amounting to roughly $80,000 per victim was publicly dismissed by families as “insulting.” Many of them say they have suffered profound emotional and economic loss.