Director Joel Souza has been released from the hospital following an injury on the set of his upcoming western film Rust

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Director Joel Souza has been released from the hospital following an injury after Alec Baldwin accidentally misfired a prop gun on the New Mexico set of his upcoming western film Rust.

On Thursday, the Santa Fe Sheriff's Department announced in a press release that Souza, 48, was injured on set after Baldwin, 63, discharged a prop firearm. Officials previously said Souza was undergoing treatment for his injuries at Christus St. Vincent's hospital Thursday night. 

On Friday, reps of the filmmaker confirmed his release to Deadline. Actress Frances Fisher also shared the news in a series of tweets.

In response to Patricia Arquette's social media condolences following the accident, Fisher responded, "Director Joel Souza told me he's out of hospital."

The actress later asserted again that Souza was no longer in the hospital and was released "hours ago."

Representatives for Joel Souza did not immediately respond to PEOPLE's request for comment.

Joel Souza; Alec Baldwin
Credit: Ron Adar/SOPA Images/Shutterstock; Mark Sagliocco/Getty Images

Along with the Rust director's injury, Thursday's tragic accident killed cinematographer Halyna Hutchins, 42, who was airlifted to the University of New Mexico Hospital and later died from her injuries, according to the sheriff's department.

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Following Hutchins' death, directors, actors and those in the film industry paid tribute to the late cinematographer.

"She was an absolutely incredible talent and a great person. She had such an eye and a visual style, she was the kind of cinematographer that you wanted to see succeed because you wanted to see what she could pull off next," wrote actor Joe Manganiello on Instagram, "and she was a fantastic person."

So far, no charges have been filed. The investigation into the incident remains ongoing.

Alec Baldwin; Halyna Hutchins; Joel Souza
Alec Baldwin; Halyna Hutchins; Joel Souza
| Credit: Mark Sagliocco/Getty Images; Mat Hayward/Getty Images; Ron Adar/SOPA Images/Shutterstock

The film set has now been shut down, with production indefinitely paused, according to the film's production company, Rust Movie Productions LLC.

"The entire cast and crew has been absolutely devastated by today's tragedy, and we send our deepest condolences to Halyna's family and loved ones," Rust Movie Productions LLC said in a statement. "We have halted production on the film for an undetermined period of time and are fully cooperating with the Santa Fe Police Department's investigation. We will be providing counseling services to everyone connected to the film as we work to process this awful event."

The film, written and directed by Souza, is reportedly set in 1880s Kansas. Baldwin stars as an infamous outlaw who goes on the run with his 13-year-old grandson after the teenager is convicted for the accidental murder of a local rancher and sentenced to hang, according to Deadline.