The family of a woman shot by actor Alec Baldwin on the set of the movie "Rust" sued Baldwin on Tuesday, claiming "substantial" damages for her wrongful death, AFP reported.

Baldwin was holding a Colt gun during a rehearsal for the Western in New Mexico in October when it discharged a live round, hitting cinematographer Halyna Hutchins and director Joel Souza. Hutchins later died in hospital of her wounds.

At a press conference Tuesday, lawyer Brian Panish alleged the "reckless conduct and cost-cutting measures" of Baldwin and the other "Rust" producers had led to Hutchins' death.

The attorney representing Hutchins' husband Matthew and son Andros also presented a list of "at least 15 industry standards" he said the producers had ignored on set.

These included failure to use a prop gun rather than a live weapon, a lack of individuals qualified to handle weapons on set at the time of the shooting, and lack of protective equipment for crew.

Panish also alleged that Baldwin had "refused" training on cross-drawing the gun. He presented a 3D animated reconstruction of the shooting.

Asked what level of compensation the family would seek, Panish replied, "We believe it is going to be substantial."

According to court records, the movie’s assistant director Dave Halls handed the gun to Baldwin and yelled, "Cold gun," indicating that it was loaded with blanks.

Santa Fe County District Attorney Mary Carmack-Altwies indicated shortly after the incident that criminal charges have not been ruled out in the incident.

Baldwin has said that he had no idea how a live bullet got onto the set.

"Someone is responsible for what happened, and I can’t say who that is, but it’s not me," Baldwin said in an interview following the incident, adding, "Honest to god, if I felt I was responsible, I might have killed myself."