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Alec Baldwin 'Canceling Other Projects' After Rust Shooting Death, 'Inconsolable for Hours' Says Source

Alec Baldwin attends the World Premiere of National Geographic Documentary Films' 'The First Wave' at Hamptons International Film Festival on October 07, 2021 in East Hampton, New York.
Alec Baldwin attends the World Premiere of National Geographic Documentary Films' 'The First Wave' at Hamptons International Film Festival on October 07, 2021 in East Hampton, New York.

Mark Sagliocco/Getty

Alec Baldwin "is canceling other projects" following an accidental shooting on the set of his film, Rust, that left cinematographer Halyna Hutchins dead and director Joel Souza injured.

A source tells PEOPLE that Baldwin, 63, is looking "to take some time to himself and re-center himself," as he has during difficult times in the past.

"This was pretty devastating," the source says. "This is how he handles difficult times. Whenever something bad happens, in the short term, he removes himself from [the] public eye."

The source confirms to PEOPLE that Baldwin was "hysterical and absolutely inconsolable for hours" following the shooting: "Everyone knows this was an accident, but he's absolutely devastated.

RELATED: Alec Baldwin 'Trying to Get His Head Around' Rust Shooting: 'This Has Been Devastating' (Source)

On Thursday, authorities responded to an incident at the New Mexico set of Rust around 1:50 p.m. local time following 911 calls indicating "an individual had been shot on set," the Santa Fe Sheriff's Department wrote in a press release obtained by PEOPLE.

For more on the shooting on the Rust set, listen below to our daily podcast PEOPLE Every Day.

Upon further investigation, the sheriff's department learned that Hutchins, 42, and Souza, 48, were "shot when a prop firearm was discharged" by Baldwin, 63, during a camera test.

Alec Baldwin - Halyna Hutchins
Alec Baldwin - Halyna Hutchins

Jim Spellman/Getty; Fred Hayes/Getty

Hutchins was airlifted to the University of New Mexico Hospital where she died from her injuries, according to the sheriff's department. Souza was hospitalized, but his reps told Deadline he has since been released.

"[Baldwin] is someone who really deeply cares, so he can be very hard on himself," the source shares. "That's true in general, in situations nowhere near as serious as this. But in this situation, it's a whole other level because of the loss of life involved."

"It's going to take him time to figure all this out," they add. "He needs to take a while to himself, to be with his family."

So far, no charges have been filed and an investigation remains ongoing.

RELATED: 911 Call Reveals Details About Alec Baldwin's On-Set Shooting Accident: 'We Need Help Immediately'

In the wake of the tragedy, a source previously told PEOPLE that "Alec is still trying to get his head around everything that happened. This has been devastating. It's been incredibly difficult."

Baldwin first spoke out regarding the incident on Friday morning, issuing a two-part statement on Twitter.

"There are no words to convey my shock and sadness regarding the tragic accident that took the life of Halyna Hutchins, a wife, mother and deeply admired colleague of ours," the actor began.

RELATED VIDEO: Alec Baldwin Seen Distraught After Accidental Shooting on Set of Rust Movie, Killing Cinematographer

"I'm fully cooperating with the police investigation to address how this tragedy occurred and I am in touch with her husband, offering my support to him and his family," he continued. "My heart is broken for her husband, their son, and all who knew and loved Halyna."

Hutchins' husband Matthew, with whom she shares 9-year-old son Andros, has since been in contact with Baldwin. "I have spoken with Alec Baldwin and he is being very supportive," Matthew told the Daily Mail.

RELATED: Halyna Hutchins' Husband Matthew Honors His Late Wife in First Instagram Post Since Her Death: 'We Miss You'

The Rust film set has been shut down following Hutchins' death, with production indefinitely paused, according to the 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," the company said in a statement on Thursday. "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."

For more on the shooting on the Rust set, listen below to our daily podcast PEOPLE Every Day.