Alec Baldwin's lawyer called the claim that the actor was "reckless" on the set of "Rust" "entirely false" in a statement to Fox News Digital.

Baldwin was named in a wrongful death lawsuit filed by cinematographer Halyna Hutchins' family Tuesday. Hutchins died on the set of "Rust" on Oct. 21 after a gun Baldwin was holding discharged.

The Hutchins family's lead lawyer Brian Panish claimed "reckless behavior and cost-cutting" led to the death of Hutchins during a press conference regarding the lawsuit.

However, Baldwin's attorney hit back at the claim as he emphasized that the actor is continuing to "cooperate" with authorities on the investigation into Hutchins' death.

Alec Baldwin's lawyer called the claim that the actor was "reckless" on the set of "Rust" "entirely false" in a statement to Fox News Digital. (Fox News Digital)

ALEC BALDWIN, OTHERS ‘RESPONSIBLE’ FOR HALYNA HUTCHINS' DEATH IN ‘RUST’ SHOOTING: WRONGFUL DEATH LAWSUIT

"Everyone’s hearts and thoughts remain with Halyna’s family as they continue to process this unspeakable tragedy. We continue to cooperate with the authorities to determine how live ammunition arrived on the ‘Rust’ set in the first place. Any claim that Alec was reckless is entirely false," attorney Aaron Dyer said on behalf of Baldwin in a statement to Fox News Digital.

"He, Halyna and the rest of the crew relied on the statement by the two professionals responsible for checking the gun that it was a ‘cold gun’ — meaning there is no possibility of a discharge, blank or otherwise. This protocol has worked on thousands of films, with millions of discharges, as there has never before been an incident on a set where an actual bullet harmed anyone. Actors should be able to rely on armorers and prop department professionals, as well as assistant directors, rather than deciding on their own when a gun is safe to use."

Baldwin, armorer Hannah Gutierrez-Reed, assistant director David Halls, production companies and producers were named in the lawsuit filed on behalf of Halyna's husband Matthew Hutchins and their son Andros on Tuesday in New Mexico.

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Cinematographer Halyna Hutchins died on the set of "Rust" on Oct. 21 after a gun Baldwin was holding discharged. (Photo by Sam Wasson/Getty Images  |  Photo by Fred Hayes/Getty Images for SAGindie)

Representatives for Gutierrez Reed and Halls did not immediately respond to Fox News Digital's request for comment.

The Santa Fe County Sheriff's office, which is conducting the investigation into Hutchins' death, had no comment on the lawsuit filed.

"The investigation remains open and ongoing," Juan Rios, a spokesperson for the sheriff's office, told Fox News Digital.

Despite naming others in the lawsuit, the Hutchins family's lawyer pointed most blame on Baldwin himself.

"I think it's clear what happened," Panish told reporters Tuesday. "Alec had the gun in his hand. He shot it. Halyna was killed."

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Hutchins' family filed a wrongful death lawsuit naming Baldwin among others Tuesday in New Mexico. (AP/Getty Images)

He also claimed that Baldwin had refused weapons training on how to cross-draw a revolver. Per Panish, Baldwin and production had "disregarded at least 15 industry standards" on the set of "Rust."

Hutchins' family is suing for punitive damages, funeral and burial expenses, among other things to be determined at trial.

"Halyna Hutchins deserved to live, and the Defendants had the power to prevent her death if they had only held sacrosanct their duty to protect the safety of every individual on a set where firearms were present instead of cutting corners on safety procedures where human lives were at stake, rushing to stay on schedule and ignoring numerous complaints of safety violations," the lawsuit reads.

"This lawsuit seeks justice for the losses of her survivors and to hold responsible those who caused her tragic death."

Baldwin was spotted running errands in New York City on Tuesday morning ahead of the wrongful death lawsuit announcement.